LMFDB - Embedded newform 425.3.u.d.401.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.8
Character	$\chi$	$=$	425.401
Dual form			425.3.u.d.301.8

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.467086 - 1.12765i) q^{2} +(0.162239 + 0.108405i) q^{3} +(1.77501 + 1.77501i) q^{4} +(0.198022 - 0.132314i) q^{6} +(-0.551755 - 0.109751i) q^{7} +(7.34125 - 3.04085i) q^{8} +(-3.42958 - 8.27974i) q^{9} +(-10.3431 - 15.4795i) q^{11} +(0.0955567 + 0.480396i) q^{12} +(1.47521 - 1.47521i) q^{13} +(-0.381477 + 0.570921i) q^{14} +0.342319i q^{16} +(6.51358 + 15.7027i) q^{17} -10.9385 q^{18} +(10.3872 - 25.0770i) q^{19} +(-0.0776188 - 0.0776188i) q^{21} +(-22.2866 + 4.43307i) q^{22} +(37.3309 - 24.9437i) q^{23} +(1.52068 + 0.302482i) q^{24} +(-0.974463 - 2.35256i) q^{26} +(0.683751 - 3.43745i) q^{27} +(-0.784563 - 1.17418i) q^{28} +(7.35634 + 36.9828i) q^{29} +(22.5110 - 33.6901i) q^{31} +(29.7510 + 12.3233i) q^{32} -3.63263i q^{33} +(20.7494 - 0.0105167i) q^{34} +(8.60909 - 20.7842i) q^{36} +(25.4910 + 17.0326i) q^{37} +(-23.4262 - 23.4262i) q^{38} +(0.399256 - 0.0794170i) q^{39} +(-4.83333 - 0.961410i) q^{41} +(-0.123781 + 0.0512718i) q^{42} +(-18.3947 - 44.4087i) q^{43} +(9.11725 - 45.8355i) q^{44} +(-10.6909 - 53.7469i) q^{46} +(-57.3767 + 57.3767i) q^{47} +(-0.0371090 + 0.0555375i) q^{48} +(-44.9777 - 18.6304i) q^{49} +(-0.645485 + 3.25369i) q^{51} +5.23702 q^{52} +(-5.95470 + 14.3759i) q^{53} +(-3.55685 - 2.37661i) q^{54} +(-4.38431 + 0.872094i) q^{56} +(4.40368 - 2.94245i) q^{57} +(45.1396 + 8.97882i) q^{58} +(-63.0273 + 26.1068i) q^{59} +(8.00992 - 40.2686i) q^{61} +(-27.4759 - 41.1206i) q^{62} +(0.983580 + 4.94479i) q^{63} +(26.8243 - 26.8243i) q^{64} +(-4.09632 - 1.69675i) q^{66} +58.1450i q^{67} +(-16.3107 + 39.4341i) q^{68} +8.76055 q^{69} +(76.9389 + 51.4089i) q^{71} +(-50.3548 - 50.3548i) q^{72} +(-66.8722 + 13.3017i) q^{73} +(31.1132 - 20.7892i) q^{74} +(62.9495 - 26.0745i) q^{76} +(4.00797 + 9.67608i) q^{77} +(0.0969328 - 0.487314i) q^{78} +(5.53158 + 8.27860i) q^{79} +(-56.5498 + 56.5498i) q^{81} +(-3.34171 + 5.00123i) q^{82} +(64.0331 + 26.5234i) q^{83} -0.275549i q^{84} -58.6692 q^{86} +(-2.81563 + 6.79752i) q^{87} +(-123.002 - 82.1874i) q^{88} +(-74.1047 - 74.1047i) q^{89} +(-0.975860 + 0.652049i) q^{91} +(110.538 + 21.9874i) q^{92} +(7.30434 - 3.02556i) q^{93} +(37.9007 + 91.5005i) q^{94} +(3.49088 + 5.22447i) q^{96} +(-30.1730 - 151.690i) q^{97} +(-42.0169 + 42.0169i) q^{98} +(-92.6941 + 138.726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{12} + 24 q^{13} + 32 q^{14} - 8 q^{17} - 64 q^{18} - 24 q^{19} - 96 q^{22} - 56 q^{23} - 336 q^{24} - 224 q^{26} + 144 q^{27} - 480 q^{28} - 64 q^{31} + 40 q^{32} + 64 q^{34} + 192 q^{36} - 128 q^{37}+ \cdots - 160 q^{99}+O(q^{100}) $ 96 * q + 96 * q^12 + 24 * q^13 + 32 * q^14 - 8 * q^17 - 64 * q^18 - 24 * q^19 - 96 * q^22 - 56 * q^23 - 336 * q^24 - 224 * q^26 + 144 * q^27 - 480 * q^28 - 64 * q^31 + 40 * q^32 + 64 * q^34 + 192 * q^36 - 128 * q^37 + 496 * q^38 + 16 * q^39 + 216 * q^41 - 432 * q^42 + 592 * q^43 - 32 * q^44 + 336 * q^46 + 160 * q^48 - 32 * q^49 - 32 * q^51 - 96 * q^53 + 584 * q^54 - 40 * q^56 - 1120 * q^57 - 256 * q^58 + 544 * q^59 + 112 * q^61 - 560 * q^62 - 312 * q^63 + 592 * q^64 - 24 * q^66 - 192 * q^69 - 336 * q^71 + 1040 * q^72 - 336 * q^74 - 1016 * q^76 + 960 * q^77 - 384 * q^79 - 928 * q^81 + 1200 * q^82 + 144 * q^83 + 64 * q^86 + 672 * q^87 + 832 * q^88 + 576 * q^89 + 336 * q^91 + 1008 * q^92 + 512 * q^93 + 672 * q^94 + 768 * q^96 + 128 * q^97 + 408 * q^98 - 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.467086	−	1.12765i	0.233543	−	0.563823i	−0.763046	−	0.646344i	$-0.776297\pi$
$2$	0.467086	−	1.12765i	0.233543	−	0.563823i	0.996589	+	0.0825211i	$0.0262972\pi$
$3$	0.162239	+	0.108405i	0.0540797	+	0.0361349i	0.582316	−	0.812962i	$-0.302147\pi$
$3$	0.162239	+	0.108405i	0.0540797	+	0.0361349i	−0.528237	+	0.849097i	$0.677147\pi$
$4$	1.77501	+	1.77501i	0.443753	+	0.443753i
$5$		0			0
$5$		0			0
$6$	0.198022	−	0.132314i	0.0330036	−	0.0220523i
$7$	−0.551755	−	0.109751i	−0.0788222	−	0.0156787i	0.155522	−	0.987832i	$-0.450294\pi$
$7$	−0.551755	−	0.109751i	−0.0788222	−	0.0156787i	−0.234344	+	0.972154i	$0.575294\pi$
$8$	7.34125	−	3.04085i	0.917656	−	0.380106i
$9$	−3.42958	−	8.27974i	−0.381065	−	0.919971i
$10$		0			0
$11$	−10.3431	−	15.4795i	−0.940282	−	1.40723i	−0.913161	−	0.407599i	$-0.866366\pi$
$11$	−10.3431	−	15.4795i	−0.940282	−	1.40723i	−0.0271204	−	0.999632i	$-0.508634\pi$
$12$	0.0955567	+	0.480396i	0.00796306	+	0.0400330i
$13$	1.47521	−	1.47521i	0.113478	−	0.113478i	−0.648088	−	0.761565i	$-0.724431\pi$
$13$	1.47521	−	1.47521i	0.113478	−	0.113478i	0.761565	+	0.648088i	$0.224431\pi$
$14$	−0.381477	+	0.570921i	−0.0272484	+	0.0407801i
$15$		0			0
$16$			0.342319i			0.0213949i
$17$	6.51358	+	15.7027i	0.383152	+	0.923685i
$17$	6.51358	+	15.7027i	0.383152	+	0.923685i
$18$	−10.9385			−0.607696
$19$	10.3872	−	25.0770i	0.546697	−	1.31984i	−0.373225	−	0.927741i	$-0.621748\pi$
$19$	10.3872	−	25.0770i	0.546697	−	1.31984i	0.919922	−	0.392102i	$-0.128252\pi$
$20$		0			0
$21$	−0.0776188	−	0.0776188i	−0.00369613	−	0.00369613i
$22$	−22.2866	+	4.43307i	−1.01303	+	0.201503i
$23$	37.3309	−	24.9437i	1.62308	−	1.08451i	0.690634	−	0.723204i	$-0.257331\pi$
$23$	37.3309	−	24.9437i	1.62308	−	1.08451i	0.932448	−	0.361305i	$-0.117669\pi$
$24$	1.52068	+	0.302482i	0.0633617	+	0.0126034i
$25$		0			0
$26$	−0.974463	−	2.35256i	−0.0374793	−	0.0904831i
$27$	0.683751	−	3.43745i	0.0253241	−	0.127313i
$28$	−0.784563	−	1.17418i	−0.0280201	−	0.0419351i
$29$	7.35634	+	36.9828i	0.253667	+	1.27527i	0.872059	+	0.489400i	$0.162784\pi$
$29$	7.35634	+	36.9828i	0.253667	+	1.27527i	−0.618392	+	0.785870i	$0.712216\pi$
$30$		0			0
$31$	22.5110	−	33.6901i	0.726162	−	1.08678i	−0.266260	−	0.963901i	$-0.585788\pi$
$31$	22.5110	−	33.6901i	0.726162	−	1.08678i	0.992422	−	0.122877i	$-0.0392120\pi$
$32$	29.7510	+	12.3233i	0.929719	+	0.385102i
$33$		−	3.63263i		−	0.110080i
$34$	20.7494	−	0.0105167i	0.610277	−	0.000309315i
$35$		0			0
$36$	8.60909	−	20.7842i	0.239141	−	0.577339i
$37$	25.4910	+	17.0326i	0.688946	+	0.460339i	0.850121	−	0.526587i	$-0.176528\pi$
$37$	25.4910	+	17.0326i	0.688946	+	0.460339i	−0.161175	+	0.986926i	$0.551528\pi$
$38$	−23.4262	−	23.4262i	−0.616480	−	0.616480i
$39$	0.399256	−	0.0794170i	0.0102373	−	0.00203633i
$40$		0			0
$41$	−4.83333	−	0.961410i	−0.117886	−	0.0234490i	0.135795	−	0.990737i	$-0.456641\pi$
$41$	−4.83333	−	0.961410i	−0.117886	−	0.0234490i	−0.253681	+	0.967288i	$0.581641\pi$
$42$	−0.123781	+	0.0512718i	−0.00294717	+	0.00122076i
$43$	−18.3947	−	44.4087i	−0.427783	−	1.03276i	−0.979989	−	0.199052i	$-0.936214\pi$
$43$	−18.3947	−	44.4087i	−0.427783	−	1.03276i	0.552206	−	0.833708i	$-0.313786\pi$
$44$	9.11725	−	45.8355i	0.207210	−	1.04172i
$45$		0			0
$46$	−10.6909	−	53.7469i	−0.232411	−	1.16841i
$47$	−57.3767	+	57.3767i	−1.22078	+	1.22078i	−0.253427	+	0.967355i	$0.581558\pi$
$47$	−57.3767	+	57.3767i	−1.22078	+	1.22078i	−0.967355	+	0.253427i	$0.918442\pi$
$48$	−0.0371090	+	0.0555375i	−0.000773104	+	0.00115703i
$49$	−44.9777	−	18.6304i	−0.917912	−	0.380212i
$50$		0			0
$51$	−0.645485	+	3.25369i	−0.0126566	+	0.0637978i
$52$	5.23702			0.100712
$53$	−5.95470	+	14.3759i	−0.112353	+	0.271244i	−0.970047	−	0.242916i	$-0.921896\pi$
$53$	−5.95470	+	14.3759i	−0.112353	+	0.271244i	0.857695	+	0.514160i	$0.171896\pi$
$54$	−3.55685	−	2.37661i	−0.0658676	−	0.0440113i
$55$		0			0
$56$	−4.38431	+	0.872094i	−0.0782913	+	0.0155731i
$57$	4.40368	−	2.94245i	0.0772576	−	0.0516219i
$58$	45.1396	+	8.97882i	0.778268	+	0.154807i
$59$	−63.0273	+	26.1068i	−1.06826	+	0.442487i	−0.846376	−	0.532586i	$-0.821220\pi$
$59$	−63.0273	+	26.1068i	−1.06826	+	0.442487i	−0.221883	+	0.975073i	$0.571220\pi$
$60$		0			0
$61$	8.00992	−	40.2686i	0.131310	−	0.660141i	−0.857921	−	0.513781i	$-0.828244\pi$
$61$	8.00992	−	40.2686i	0.131310	−	0.660141i	0.989231	−	0.146360i	$-0.0467557\pi$
$62$	−27.4759	−	41.1206i	−0.443160	−	0.663236i
$63$	0.983580	+	4.94479i	0.0156124	+	0.0784888i
$64$	26.8243	−	26.8243i	0.419130	−	0.419130i
$65$		0			0
$66$	−4.09632	−	1.69675i	−0.0620654	−	0.0257083i
$67$			58.1450i			0.867835i	0.900952	+	0.433918i	$0.142869\pi$
$67$			58.1450i			0.867835i	−0.900952	+	0.433918i	$0.857131\pi$
$68$	−16.3107	+	39.4341i	−0.239863	+	0.579913i
$69$	8.76055			0.126964
$70$		0			0
$71$	76.9389	+	51.4089i	1.08365	+	0.724070i	0.963237	−	0.268655i	$-0.0865790\pi$
$71$	76.9389	+	51.4089i	1.08365	+	0.724070i	0.120410	+	0.992724i	$0.461579\pi$
$72$	−50.3548	−	50.3548i	−0.699373	−	0.699373i
$73$	−66.8722	+	13.3017i	−0.916058	+	0.182215i	−0.630539	−	0.776158i	$-0.717166\pi$
$73$	−66.8722	+	13.3017i	−0.916058	+	0.182215i	−0.285519	+	0.958373i	$0.592166\pi$
$74$	31.1132	−	20.7892i	0.420448	−	0.280935i
$75$		0			0
$76$	62.9495	−	26.0745i	0.828283	−	0.343086i
$77$	4.00797	+	9.67608i	0.0520515	+	0.125663i
$78$	0.0969328	−	0.487314i	0.00124273	−	0.00624761i
$79$	5.53158	+	8.27860i	0.0700201	+	0.104792i	0.864827	−	0.502070i	$-0.167428\pi$
$79$	5.53158	+	8.27860i	0.0700201	+	0.104792i	−0.794807	+	0.606862i	$0.792428\pi$
$80$		0			0
$81$	−56.5498	+	56.5498i	−0.698146	+	0.698146i
$82$	−3.34171	+	5.00123i	−0.0407526	+	0.0609906i
$83$	64.0331	+	26.5234i	0.771483	+	0.319559i	0.733473	−	0.679719i	$-0.237898\pi$
$83$	64.0331	+	26.5234i	0.771483	+	0.319559i	0.0380102	+	0.999277i	$0.487898\pi$
$84$		−	0.275549i		−	0.00328034i
$85$		0			0
$86$	−58.6692			−0.682200
$87$	−2.81563	+	6.79752i	−0.0323635	+	0.0781325i
$88$	−123.002	−	82.1874i	−1.39775	−	0.933948i
$89$	−74.1047	−	74.1047i	−0.832637	−	0.832637i	0.155240	−	0.987877i	$-0.450385\pi$
$89$	−74.1047	−	74.1047i	−0.832637	−	0.832637i	−0.987877	+	0.155240i	$0.950385\pi$
$90$		0			0
$91$	−0.975860	+	0.652049i	−0.0107237	+	0.00716537i
$92$	110.538	+	21.9874i	1.20150	+	0.238994i
$93$	7.30434	−	3.02556i	0.0785413	−	0.0325329i
$94$	37.9007	+	91.5005i	0.403199	+	0.973409i
$95$		0			0
$96$	3.49088	+	5.22447i	0.0363633	+	0.0544215i
$97$	−30.1730	−	151.690i	−0.311062	−	1.56382i	−0.747612	−	0.664136i	$-0.768800\pi$
$97$	−30.1730	−	151.690i	−0.311062	−	1.56382i	0.436550	−	0.899680i	$-0.356200\pi$
$98$	−42.0169	+	42.0169i	−0.428744	+	0.428744i
$99$	−92.6941	+	138.726i	−0.936304	+	1.40128i
$100$		0			0
$101$		−	83.0452i		−	0.822230i	−0.911583	−	0.411115i	$-0.865139\pi$
$101$		−	83.0452i		−	0.822230i	0.911583	−	0.411115i	$-0.134861\pi$
$102$	3.36751	+	2.24763i	0.0330148	+	0.0220356i
$103$	95.8462			0.930546			0.465273	−	0.885167i	$-0.345956\pi$
$103$	95.8462			0.930546			0.465273	+	0.885167i	$0.345956\pi$
$104$	6.34399	−	15.3158i	0.0609999	−	0.147267i
$105$		0			0
$106$	13.4296	+	13.4296i	0.126694	+	0.126694i
$107$	71.7653	−	14.2750i	0.670704	−	0.133411i	0.152020	−	0.988377i	$-0.451422\pi$
$107$	71.7653	−	14.2750i	0.670704	−	0.133411i	0.518684	+	0.854966i	$0.326422\pi$
$108$	7.31518	−	4.88785i	0.0677331	−	0.0452578i
$109$	45.3495	+	9.02057i	0.416050	+	0.0827576i	0.398677	−	0.917092i	$-0.369470\pi$
$109$	45.3495	+	9.02057i	0.416050	+	0.0827576i	0.0173736	+	0.999849i	$0.494470\pi$
$110$		0			0
$111$	2.28923	+	5.52669i	0.0206237	+	0.0497900i
$112$	0.0375698	−	0.188876i	0.000335445	−	0.00168639i
$113$	28.8541	+	43.1832i	0.255346	+	0.382152i	0.936890	−	0.349625i	$-0.113691\pi$
$113$	28.8541	+	43.1832i	0.255346	+	0.382152i	−0.681544	+	0.731777i	$0.738691\pi$
$114$	−1.26114	−	6.34017i	−0.0110626	−	0.0556155i
$115$		0			0
$116$	−52.5874	+	78.7025i	−0.453339	+	0.678470i
$117$	−17.2737	−	7.15500i	−0.147638	−	0.0611538i
$118$			83.2666i			0.705649i
$119$	−1.87052	−	9.37889i	−0.0157187	−	0.0788142i
$120$		0			0
$121$	−86.3318	+	208.423i	−0.713486	+	1.72251i
$122$	−41.6674	−	27.8413i	−0.341536	−	0.228207i
$123$	−0.679934	−	0.679934i	−0.00552792	−	0.00552792i
$124$	99.7577	−	19.8430i	0.804498	−	0.160025i
$125$		0			0
$126$	6.03539	+	1.20051i	0.0478999	+	0.00952789i
$127$	−79.4211	+	32.8973i	−0.625363	+	0.259034i	−0.672781	−	0.739841i	$-0.734901\pi$
$127$	−79.4211	+	32.8973i	−0.625363	+	0.259034i	0.0474184	+	0.998875i	$0.484901\pi$
$128$	31.5740	+	76.2264i	0.246672	+	0.595519i
$129$	1.82977	−	9.19890i	0.0141843	−	0.0713093i
$130$		0			0
$131$	36.4935	+	183.465i	0.278576	+	1.40050i	0.826014	+	0.563650i	$0.190603\pi$
$131$	36.4935	+	183.465i	0.278576	+	1.40050i	−0.547438	+	0.836846i	$0.684397\pi$
$132$	6.44796	−	6.44796i	0.0488482	−	0.0488482i
$133$	−8.48344	+	12.6964i	−0.0637853	+	0.0954614i
$134$	65.5669	+	27.1587i	0.489305	+	0.202677i
$135$		0			0
$136$	95.5671	+	95.4703i	0.702700	+	0.701988i
$137$	−5.25909			−0.0383875			−0.0191938	−	0.999816i	$-0.506110\pi$
$137$	−5.25909			−0.0383875			−0.0191938	+	0.999816i	$0.506110\pi$
$138$	4.09193	−	9.87879i	0.0296517	−	0.0715854i
$139$	56.0316	+	37.4391i	0.403105	+	0.269346i	0.740553	−	0.671998i	$-0.234564\pi$
$139$	56.0316	+	37.4391i	0.403105	+	0.269346i	−0.337448	+	0.941344i	$0.609564\pi$
$140$		0			0
$141$	−15.5287	+	3.08884i	−0.110132	+	0.0219067i
$142$	93.9082	−	62.7474i	0.661325	−	0.441883i
$143$	−38.0938	−	7.57732i	−0.266390	−	0.0529883i
$144$	2.83431	−	1.17401i	0.0196827	−	0.00815285i
$145$		0			0
$146$	−16.2355	+	81.6212i	−0.111202	+	0.559050i
$147$	−5.27752	−	7.89837i	−0.0359015	−	0.0537304i
$148$	15.0139	+	75.4798i	0.101445	+	0.509999i
$149$	−90.5416	+	90.5416i	−0.607662	+	0.607662i	−0.942334	−	0.334673i	$-0.891374\pi$
$149$	−90.5416	+	90.5416i	−0.607662	+	0.607662i	0.334673	+	0.942334i	$0.391374\pi$
$150$		0			0
$151$	−128.407	−	53.1878i	−0.850375	−	0.352237i	−0.0854391	−	0.996343i	$-0.527229\pi$
$151$	−128.407	−	53.1878i	−0.850375	−	0.352237i	−0.764936	+	0.644107i	$0.777229\pi$
$152$		−	215.683i		−	1.41896i
$153$	107.675	−	107.784i	0.703759	−	0.704472i
$154$	12.7833			0.0830082
$155$		0			0
$156$	0.849650	+	0.567718i	0.00544648	+	0.00363922i
$157$	102.658	+	102.658i	0.653870	+	0.653870i	0.953923	−	0.300052i	$-0.0970042\pi$
$157$	102.658	+	102.658i	0.653870	+	0.653870i	−0.300052	+	0.953923i	$0.597004\pi$
$158$	11.9191	−	2.37085i	0.0754371	−	0.0150054i
$159$	−2.52450	+	1.68682i	−0.0158774	+	0.0106089i
$160$		0			0
$161$	−23.3351	+	9.66572i	−0.144939	+	0.0600355i
$162$	37.3545	+	90.1817i	0.230583	+	0.556677i
$163$	−13.3770	+	67.2507i	−0.0820674	+	0.412581i	0.917811	+	0.397017i	$0.129954\pi$
$163$	−13.3770	+	67.2507i	−0.0820674	+	0.412581i	−0.999879	+	0.0155642i	$0.995046\pi$
$164$	−6.87271	−	10.2857i	−0.0419068	−	0.0627179i
$165$		0			0
$166$	59.8180	−	59.8180i	0.360349	−	0.360349i
$167$	−22.9837	+	34.3975i	−0.137627	+	0.205973i	−0.893880	−	0.448305i	$-0.852028\pi$
$167$	−22.9837	+	34.3975i	−0.137627	+	0.205973i	0.756253	+	0.654279i	$0.227028\pi$
$168$	−0.805846	−	0.333792i	−0.00479670	−	0.00198686i
$169$			164.648i			0.974246i
$170$		0			0
$171$	−243.255			−1.42254
$172$	46.1752	−	111.477i	0.268460	−	0.648121i
$173$	64.2046	+	42.9002i	0.371125	+	0.247978i	0.727121	−	0.686510i	$-0.240858\pi$
$173$	64.2046	+	42.9002i	0.371125	+	0.247978i	−0.355995	+	0.934488i	$0.615858\pi$
$174$	6.35006	+	6.35006i	0.0364946	+	0.0364946i
$175$		0			0
$176$	5.29894	−	3.54064i	0.0301076	−	0.0201173i
$177$	−13.0556	−	2.59692i	−0.0737604	−	0.0146719i
$178$	−118.177	+	48.9506i	−0.663916	+	0.275003i
$179$	−30.0207	−	72.4764i	−0.167714	−	0.404896i	0.817569	−	0.575831i	$-0.195321\pi$
$179$	−30.0207	−	72.4764i	−0.167714	−	0.404896i	−0.985282	+	0.170935i	$0.945321\pi$
$180$		0			0
$181$	13.7710	+	20.6098i	0.0760829	+	0.113866i	0.867560	−	0.497333i	$-0.165687\pi$
$181$	13.7710	+	20.6098i	0.0760829	+	0.113866i	−0.791477	+	0.611199i	$0.790687\pi$
$182$	0.279469	+	1.40499i	0.00153555	+	0.00771971i
$183$	5.66483	−	5.66483i	0.0309554	−	0.0309554i
$184$	198.205	−	296.635i	1.07720	−	1.61215i
$185$		0			0
$186$		−	9.64990i		−	0.0518812i
$187$	175.699	−	263.241i	0.939568	−	1.40771i
$188$	−203.689			−1.08345
$189$	−0.754526	+	1.82159i	−0.00399220	+	0.00963803i
$190$		0			0
$191$	163.987	+	163.987i	0.858573	+	0.858573i	0.991170	−	0.132597i	$-0.0423315\pi$
$191$	163.987	+	163.987i	0.858573	+	0.858573i	−0.132597	+	0.991170i	$0.542332\pi$
$192$	7.25985	−	1.44407i	0.0378117	−	0.00752121i
$193$	220.942	−	147.629i	1.14478	−	0.764917i	0.169421	−	0.985544i	$-0.445810\pi$
$193$	220.942	−	147.629i	1.14478	−	0.764917i	0.975358	+	0.220627i	$0.0708104\pi$
$194$	−185.146	−	36.8279i	−0.954361	−	0.189834i
$195$		0			0
$196$	−46.7668	−	112.905i	−0.238606	−	0.576046i
$197$	−42.6042	+	214.186i	−0.216265	+	1.08724i	0.708212	+	0.706000i	$0.249502\pi$
$197$	−42.6042	+	214.186i	−0.216265	+	1.08724i	−0.924477	+	0.381238i	$0.875498\pi$
$198$	113.138	+	169.323i	0.571405	+	0.855168i
$199$	29.1291	+	146.442i	0.146377	+	0.735888i	0.982340	+	0.187103i	$0.0599097\pi$
$199$	29.1291	+	146.442i	0.146377	+	0.735888i	−0.835963	+	0.548786i	$0.815090\pi$
$200$		0			0
$201$	−6.30319	+	9.43339i	−0.0313592	+	0.0469323i
$202$	−93.6456	−	38.7893i	−0.463592	−	0.192026i
$203$		−	21.2128i		−	0.104497i
$204$	−6.92108	+	4.62959i	−0.0339268	+	0.0226941i
$205$		0			0
$206$	44.7684	−	108.081i	0.217323	−	0.524663i
$207$	−334.557	−	223.544i	−1.61622	−	1.07992i
$208$	0.504991	+	0.504991i	0.00242784	+	0.00242784i
$209$	−495.617	+	98.5843i	−2.37137	+	0.471695i
$210$		0			0
$211$	176.804	+	35.1685i	0.837935	+	0.166676i	0.595362	−	0.803458i	$-0.297009\pi$
$211$	176.804	+	35.1685i	0.837935	+	0.166676i	0.242573	+	0.970133i	$0.422009\pi$
$212$	−36.0871	+	14.9478i	−0.170222	+	0.0705083i
$213$	6.90953	+	16.6811i	0.0324391	+	0.0783150i
$214$	17.4234	−	87.5935i	0.0814179	−	0.409315i
$215$		0			0
$216$	−5.43316	−	27.3143i	−0.0251535	−	0.126455i
$217$	−16.1181	+	16.1181i	−0.0742770	+	0.0742770i
$218$	31.3541	−	46.9248i	0.143826	−	0.215251i
$219$	−12.2913	−	5.09121i	−0.0561245	−	0.0232475i
$220$		0			0
$221$	32.7736	+	13.5558i	0.148297	+	0.0613385i
$222$	7.30142			0.0328893
$223$	−106.229	+	256.461i	−0.476365	+	1.15005i	0.484936	+	0.874549i	$0.338843\pi$
$223$	−106.229	+	256.461i	−0.476365	+	1.15005i	−0.961302	+	0.275498i	$0.911157\pi$
$224$	−15.0628	−	10.0646i	−0.0672446	−	0.0449314i
$225$		0			0
$226$	62.1727	−	12.3669i	0.275100	−	0.0547209i
$227$	−224.585	+	150.063i	−0.989359	+	0.661069i	−0.941228	−	0.337772i	$-0.890327\pi$
$227$	−224.585	+	150.063i	−0.989359	+	0.661069i	−0.0481314	+	0.998841i	$0.515327\pi$
$228$	13.0395	+	2.59371i	0.0571907	+	0.0113759i
$229$	306.590	−	126.994i	1.33882	−	0.554558i	0.405662	−	0.914023i	$-0.367041\pi$
$229$	306.590	−	126.994i	1.33882	−	0.554558i	0.933159	+	0.359465i	$0.117041\pi$
$230$		0			0
$231$	−0.398684	+	2.00432i	−0.00172591	+	0.00867672i
$232$	166.464	+	249.131i	0.717516	+	1.07384i
$233$	−8.66799	−	43.5769i	−0.0372017	−	0.187025i	0.957716	−	0.287714i	$-0.0928953\pi$
$233$	−8.66799	−	43.5769i	−0.0372017	−	0.187025i	−0.994918	+	0.100689i	$0.967895\pi$
$234$	−16.1366	+	16.1366i	−0.0689598	+	0.0689598i
$235$		0			0
$236$	−158.214	−	65.5344i	−0.670398	−	0.277688i
$237$			1.94276i			0.00819731i
$238$	−11.4498	−	2.27147i	−0.0481083	−	0.00954398i
$239$	186.338			0.779656			0.389828	−	0.920888i	$-0.372534\pi$
$239$	186.338			0.779656			0.389828	+	0.920888i	$0.372534\pi$
$240$		0			0
$241$	−234.931	−	156.976i	−0.974817	−	0.651352i	−0.0373044	−	0.999304i	$-0.511877\pi$
$241$	−234.931	−	156.976i	−0.974817	−	0.651352i	−0.937512	+	0.347952i	$0.886877\pi$
$242$	194.703	+	194.703i	0.804559	+	0.804559i
$243$	−46.2419	+	9.19808i	−0.190296	+	0.0378522i
$244$	85.6950	−	57.2595i	0.351209	−	0.234670i
$245$		0			0
$246$	−1.08431	+	0.449137i	−0.00440778	+	0.00182576i
$247$	−21.6705	−	52.3172i	−0.0877347	−	0.211810i
$248$	62.8126	−	315.780i	0.253277	−	1.27331i
$249$	7.51342	+	11.2446i	0.0301744	+	0.0451591i
$250$		0			0
$251$	45.8555	−	45.8555i	0.182691	−	0.182691i	−0.609836	−	0.792528i	$-0.708765\pi$
$251$	45.8555	−	45.8555i	0.182691	−	0.182691i	0.792528	+	0.609836i	$0.208765\pi$
$252$	−7.03120	+	10.5229i	−0.0279016	+	0.0417577i
$253$	−772.234	−	319.870i	−3.05231	−	1.26431i
$254$			104.925i			0.413090i
$255$		0			0
$256$	252.446			0.986116
$257$	−144.119	+	347.933i	−0.560773	+	1.35383i	0.348376	+	0.937355i	$0.386733\pi$
$257$	−144.119	+	347.933i	−0.560773	+	1.35383i	−0.909149	+	0.416471i	$0.863267\pi$
$258$	−9.51843	−	6.36001i	−0.0368932	−	0.0246512i
$259$	−12.1955	−	12.1955i	−0.0470867	−	0.0470867i
$260$		0			0
$261$	280.979	−	187.744i	1.07655	−	0.719326i
$262$	223.929	+	44.5423i	0.854691	+	0.170009i
$263$	323.253	−	133.896i	1.22910	−	0.509109i	0.328806	−	0.944397i	$-0.393354\pi$
$263$	323.253	−	133.896i	1.22910	−	0.509109i	0.900291	+	0.435289i	$0.143354\pi$
$264$	−11.0463	−	26.6680i	−0.0418419	−	0.101015i
$265$		0			0
$266$	10.3545	+	15.4966i	0.0389267	+	0.0582579i
$267$	−3.98938	−	20.0560i	−0.0149415	−	0.0751160i
$268$	−103.208	+	103.208i	−0.385105	+	0.385105i
$269$	64.9248	−	97.1669i	0.241356	−	0.361215i	−0.690939	−	0.722913i	$-0.742803\pi$
$269$	64.9248	−	97.1669i	0.241356	−	0.361215i	0.932295	+	0.361698i	$0.117803\pi$
$270$		0			0
$271$		−	363.072i		−	1.33975i	−0.742474	−	0.669875i	$-0.766348\pi$
$271$		−	363.072i		−	1.33975i	0.742474	−	0.669875i	$-0.233652\pi$
$272$	−5.37531	+	2.22972i	−0.0197622	+	0.00819750i
$273$	−0.229008			−0.000838856
$274$	−2.45645	+	5.93039i	−0.00896514	+	0.0216438i
$275$		0			0
$276$	15.5501	+	15.5501i	0.0563408	+	0.0563408i
$277$	189.983	−	37.7900i	0.685860	−	0.136426i	0.160154	−	0.987092i	$-0.448801\pi$
$277$	189.983	−	37.7900i	0.685860	−	0.136426i	0.525707	+	0.850666i	$0.323801\pi$
$278$	68.3896	−	45.6965i	0.246006	−	0.164376i
$279$	−356.149	−	70.8424i	−1.27652	−	0.253915i
$280$		0			0
$281$	−144.495	−	348.841i	−0.514217	−	1.24143i	−0.941409	−	0.337268i	$-0.890497\pi$
$281$	−144.495	−	348.841i	−0.514217	−	1.24143i	0.427192	−	0.904161i	$-0.359503\pi$
$282$	−3.77010	+	18.9536i	−0.0133692	+	0.0672113i
$283$	−134.983	−	202.016i	−0.476971	−	0.713837i	0.512481	−	0.858698i	$-0.328726\pi$
$283$	−134.983	−	202.016i	−0.476971	−	0.713837i	−0.989452	+	0.144861i	$0.953726\pi$
$284$	45.3160	+	227.819i	0.159563	+	0.802180i
$285$		0			0
$286$	−26.3376	+	39.4170i	−0.0920895	+	0.137822i
$287$	2.56130	+	1.06093i	0.00892440	+	0.00369661i
$288$		−	288.594i		−	1.00206i
$289$	−204.147	+	204.561i	−0.706390	+	0.707823i
$290$		0			0
$291$	11.5487	−	27.8810i	0.0396862	−	0.0958109i
$292$	−142.310	−	95.0883i	−0.487362	−	0.325645i
$293$	129.066	+	129.066i	0.440498	+	0.440498i	0.892179	−	0.451681i	$-0.149176\pi$
$293$	129.066	+	129.066i	0.440498	+	0.440498i	−0.451681	+	0.892179i	$0.649176\pi$
$294$	−11.3716	+	2.26196i	−0.0386790	+	0.00769373i
$295$		0			0
$296$	238.929	+	47.5260i	0.807193	+	0.160561i
$297$	−60.2822	+	24.9697i	−0.202970	+	0.0840731i
$298$	59.8081	+	144.390i	0.200698	+	0.484529i
$299$	18.2737	−	91.8680i	0.0611160	−	0.307251i
$300$		0			0
$301$	5.27547	+	26.5216i	0.0175265	+	0.0881115i
$302$	−119.954	+	119.954i	−0.397198	+	0.397198i
$303$	9.00250	−	13.4732i	0.0297112	−	0.0444660i
$304$	8.58433	+	3.55575i	0.0282379	+	0.0116965i
$305$		0			0
$306$	−71.2489	−	171.764i	−0.232840	−	0.561320i
$307$	−131.445			−0.428159			−0.214080	−	0.976816i	$-0.568675\pi$
$307$	−131.445			−0.428159			−0.214080	+	0.976816i	$0.568675\pi$
$308$	−10.0610	+	24.2894i	−0.0326655	+	0.0788615i
$309$	15.5500	+	10.3902i	0.0503237	+	0.0336252i
$310$		0			0
$311$	16.4888	−	3.27982i	0.0530185	−	0.0105460i	−0.168510	−	0.985700i	$-0.553895\pi$
$311$	16.4888	−	3.27982i	0.0530185	−	0.0105460i	0.221528	+	0.975154i	$0.428895\pi$
$312$	2.68954	−	1.79710i	0.00862033	−	0.00575992i
$313$	58.4595	+	11.6283i	0.186771	+	0.0371512i	0.287590	−	0.957754i	$-0.407146\pi$
$313$	58.4595	+	11.6283i	0.186771	+	0.0371512i	−0.100818	+	0.994905i	$0.532146\pi$
$314$	163.711	−	67.8115i	0.521374	−	0.215960i
$315$		0			0
$316$	−4.87599	+	24.5132i	−0.0154303	+	0.0775736i
$317$	−88.3105	−	132.166i	−0.278582	−	0.416927i	0.665622	−	0.746289i	$-0.268166\pi$
$317$	−88.3105	−	132.166i	−0.278582	−	0.416927i	−0.944204	+	0.329362i	$0.893166\pi$
$318$	0.722974	+	3.63463i	0.00227350	+	0.0114297i
$319$	496.390	−	496.390i	1.55608	−	1.55608i
$320$		0			0
$321$	13.1906	+	5.46373i	0.0410923	+	0.0170210i
$322$			30.8285i			0.0957406i
$323$	461.434	−	0.233875i	1.42859	−	0.000724070i
$324$	−200.753			−0.619608
$325$		0			0
$326$	69.5867	+	46.4964i	0.213456	+	0.142627i
$327$	6.37959	+	6.37959i	0.0195094	+	0.0195094i
$328$	−38.4062	+	7.63947i	−0.117092	+	0.0232911i
$329$	37.9551	−	25.3608i	0.115365	−	0.0770844i
$330$		0			0
$331$	367.691	−	152.303i	1.11085	−	0.460129i	0.249620	−	0.968344i	$-0.419694\pi$
$331$	367.691	−	152.303i	1.11085	−	0.460129i	0.861230	+	0.508215i	$0.169694\pi$
$332$	66.5802	+	160.739i	0.200543	+	0.484153i
$333$	53.6016	−	269.473i	0.160966	−	0.809230i
$334$	28.0529	+	41.9841i	0.0839906	+	0.125701i
$335$		0			0
$336$	0.0265704	−	0.0265704i	7.90785e−5	−	7.90785e-5i
$337$	−19.2955	+	28.8778i	−0.0572568	+	0.0856908i	−0.858993	−	0.511987i	$-0.828910\pi$
$337$	−19.2955	+	28.8778i	−0.0572568	+	0.0856908i	0.801737	+	0.597678i	$0.203910\pi$
$338$	185.664	+	76.9046i	0.549302	+	0.227528i
$339$			10.1339i			0.0298936i
$340$		0			0
$341$	−754.341			−2.21214
$342$	−113.621	+	274.305i	−0.332225	+	0.802063i
$343$	45.6920	+	30.5304i	0.133213	+	0.0890100i
$344$	−270.080	−	270.080i	−0.785116	−	0.785116i
$345$		0			0
$346$	78.3653	−	52.3620i	0.226489	−	0.151335i
$347$	433.233	+	86.1754i	1.24851	+	0.248344i	0.774726	−	0.632297i	$-0.217888\pi$
$347$	433.233	+	86.1754i	1.24851	+	0.248344i	0.473784	+	0.880641i	$0.342888\pi$
$348$	−17.0635	+	7.06792i	−0.0490329	+	0.0203101i
$349$	−30.5308	−	73.7080i	−0.0874809	−	0.211198i	0.874084	−	0.485774i	$-0.161462\pi$
$349$	−30.5308	−	73.7080i	−0.0874809	−	0.211198i	−0.961565	+	0.274577i	$0.911462\pi$
$350$		0			0
$351$	−4.06228	−	6.07963i	−0.0115734	−	0.0173209i
$352$	−116.959	−	587.993i	−0.332270	−	1.67043i
$353$	−159.723	+	159.723i	−0.452474	+	0.452474i	−0.896175	−	0.443701i	$-0.853665\pi$
$353$	−159.723	+	159.723i	−0.452474	+	0.452474i	0.443701	+	0.896175i	$0.353665\pi$
$354$	−9.02649	+	13.5091i	−0.0254986	+	0.0381613i
$355$		0			0
$356$		−	263.073i		−	0.738970i
$357$	0.713245	−	1.72440i	0.00199788	−	0.00483024i
$358$	−95.7500			−0.267458
$359$	−60.3749	+	145.758i	−0.168175	+	0.406011i	−0.985388	−	0.170325i	$-0.945518\pi$
$359$	−60.3749	+	145.758i	−0.168175	+	0.406011i	0.817213	+	0.576336i	$0.195518\pi$
$360$		0			0
$361$	−265.696	−	265.696i	−0.736001	−	0.736001i
$362$	29.6728	−	5.90228i	0.0819690	−	0.0163046i
$363$	−36.6005	+	24.4557i	−0.100828	+	0.0673709i
$364$	−2.88956	−	0.574768i	−0.00793834	−	0.00157903i
$365$		0			0
$366$	−3.74196	−	9.03389i	−0.0102239	−	0.0246827i
$367$	−135.457	+	680.986i	−0.369092	+	1.85555i	0.133534	+	0.991044i	$0.457368\pi$
$367$	−135.457	+	680.986i	−0.369092	+	1.85555i	−0.502625	+	0.864504i	$0.667632\pi$
$368$	8.53870	+	12.7791i	0.0232030	+	0.0347257i
$369$	8.61608	+	43.3160i	0.0233498	+	0.117387i
$370$		0			0
$371$	4.86331	−	7.27846i	0.0131086	−	0.0196185i
$372$	18.3357	+	7.59489i	0.0492895	+	0.0204164i
$373$			79.2790i			0.212544i	0.994337	+	0.106272i	$0.0338915\pi$
$373$			79.2790i			0.212544i	−0.994337	+	0.106272i	$0.966109\pi$
$374$	−214.776	−	321.083i	−0.574268	−	0.858510i
$375$		0			0
$376$	−246.743	+	595.691i	−0.656232	+	1.58428i
$377$	65.4095	+	43.7052i	0.173500	+	0.115929i
$378$	1.70168	+	1.70168i	0.00450179	+	0.00450179i
$379$	414.708	−	82.4905i	1.09422	−	0.217653i	0.385191	−	0.922837i	$-0.374136\pi$
$379$	414.708	−	82.4905i	1.09422	−	0.217653i	0.709024	+	0.705184i	$0.249136\pi$
$380$		0			0
$381$	−16.4514	−	3.27239i	−0.0431796	−	0.00858896i
$382$	261.516	−	108.323i	0.684597	−	0.283569i
$383$	−160.880	−	388.399i	−0.420052	−	1.01410i	−0.982332	−	0.187148i	$-0.940075\pi$
$383$	−160.880	−	388.399i	−0.420052	−	1.01410i	0.562280	−	0.826947i	$-0.309925\pi$
$384$	−3.14076	+	15.7897i	−0.00817907	+	0.0411190i
$385$		0			0
$386$	−63.2740	−	318.100i	−0.163922	−	0.824093i
$387$	−304.606	+	304.606i	−0.787097	+	0.787097i
$388$	215.694	−	322.809i	0.555913	−	0.831983i
$389$	−8.41530	−	3.48573i	−0.0216332	−	0.00896075i	0.371841	−	0.928297i	$-0.378727\pi$
$389$	−8.41530	−	3.48573i	−0.0216332	−	0.00896075i	−0.393474	+	0.919336i	$0.628727\pi$
$390$		0			0
$391$	634.840	+	423.721i	1.62363	+	1.08369i
$392$	−386.845			−0.986849
$393$	−13.9678	+	33.7213i	−0.0355415	+	0.0858047i
$394$	221.626	+	148.086i	0.562503	+	0.375852i
$395$		0			0
$396$	−410.774	+	81.7081i	−1.03731	+	0.206334i
$397$	567.381	−	379.112i	1.42917	−	0.954942i	0.430545	−	0.902569i	$-0.358322\pi$
$397$	567.381	−	379.112i	1.42917	−	0.954942i	0.998628	−	0.0523730i	$-0.0166785\pi$
$398$	178.740	+	35.5536i	0.449096	+	0.0893308i
$399$	−2.75269	+	1.14020i	−0.00689898	+	0.00285765i
$400$		0			0
$401$	7.31111	−	36.7554i	0.0182322	−	0.0916594i	−0.970598	−	0.240707i	$-0.922621\pi$
$401$	7.31111	−	36.7554i	0.0182322	−	0.0916594i	0.988830	+	0.149048i	$0.0476207\pi$
$402$	7.69339	+	11.5140i	0.0191378	+	0.0286417i
$403$	−16.4915	−	82.9084i	−0.0409218	−	0.205728i
$404$	147.406	−	147.406i	0.364867	−	0.364867i
$405$		0			0
$406$	−23.9206	−	9.90822i	−0.0589176	−	0.0244045i
$407$		−	570.758i		−	1.40235i
$408$	5.15530	+	25.8490i	0.0126355	+	0.0633553i
$409$	287.263			0.702355			0.351177	−	0.936309i	$-0.385781\pi$
$409$	287.263			0.702355			0.351177	+	0.936309i	$0.385781\pi$
$410$		0			0
$411$	−0.853231	−	0.570111i	−0.00207599	−	0.00138713i
$412$	170.128	+	170.128i	0.412933	+	0.412933i
$413$	37.6409	−	7.48724i	0.0911402	−	0.0181289i
$414$	−408.345	+	272.847i	−0.986340	+	0.659051i
$415$		0			0
$416$	62.0683	−	25.7095i	0.149203	−	0.0618018i
$417$	5.03194	+	12.1482i	0.0120670	+	0.0291323i
$418$	−120.328	+	604.928i	−0.287865	+	1.44720i
$419$	222.252	+	332.624i	0.530435	+	0.793853i	0.995828	−	0.0912517i	$-0.0290868\pi$
$419$	222.252	+	332.624i	0.530435	+	0.793853i	−0.465392	+	0.885104i	$0.654087\pi$
$420$		0			0
$421$	−361.680	+	361.680i	−0.859098	+	0.859098i	−0.991232	−	0.132134i	$-0.957817\pi$
$421$	−361.680	+	361.680i	−0.859098	+	0.859098i	0.132134	+	0.991232i	$0.457817\pi$
$422$	122.240	−	182.946i	0.289669	−	0.433521i
$423$	671.842	+	278.286i	1.58828	+	0.657887i
$424$			123.645i			0.291614i
$425$		0			0
$426$	22.0377			0.0517317
$427$	−8.83904	+	21.3393i	−0.0207003	+	0.0499750i
$428$	152.723	+	102.046i	0.356828	+	0.238425i
$429$	−5.35888	−	5.35888i	−0.0124916	−	0.0124916i
$430$		0			0
$431$	477.274	−	318.904i	1.10736	−	0.739917i	0.139208	−	0.990263i	$-0.455544\pi$
$431$	477.274	−	318.904i	1.10736	−	0.739917i	0.968156	+	0.250346i	$0.0805443\pi$
$432$	1.17670	+	0.234061i	0.00272385	+	0.000541807i
$433$	−178.670	+	74.0075i	−0.412633	+	0.170918i	−0.579336	−	0.815089i	$-0.696688\pi$
$433$	−178.670	+	74.0075i	−0.412633	+	0.170918i	0.166703	+	0.986007i	$0.446688\pi$
$434$	10.6470	+	25.7040i	0.0245322	+	0.0592259i
$435$		0			0
$436$	64.4842	+	96.5075i	0.147900	+	0.221347i
$437$	−237.749	−	1195.24i	−0.544047	−	2.73511i
$438$	−11.4822	+	11.4822i	−0.0262150	+	0.0262150i
$439$	−123.464	+	184.777i	−0.281239	+	0.420904i	−0.945015	−	0.327028i	$-0.893953\pi$
$439$	−123.464	+	184.777i	−0.281239	+	0.420904i	0.663776	+	0.747932i	$0.268953\pi$
$440$		0			0
$441$			436.298i			0.989338i
$442$	30.5942	−	30.6252i	0.0692177	−	0.0692879i
$443$	−252.971			−0.571040			−0.285520	−	0.958373i	$-0.592166\pi$
$443$	−252.971			−0.571040			−0.285520	+	0.958373i	$0.592166\pi$
$444$	−5.74653	+	13.8734i	−0.0129426	+	0.0312463i
$445$		0			0
$446$	239.578	+	239.578i	0.537171	+	0.537171i
$447$	−24.5045	+	4.87425i	−0.0548200	+	0.0109044i
$448$	−17.7445	+	11.8565i	−0.0396082	+	0.0264654i
$449$	−302.898	−	60.2501i	−0.674605	−	0.134187i	−0.154112	−	0.988053i	$-0.549252\pi$
$449$	−302.898	−	60.2501i	−0.674605	−	0.134187i	−0.520493	+	0.853866i	$0.674252\pi$
$450$		0			0
$451$	35.1095	+	84.7617i	0.0778480	+	0.187942i
$452$	−25.4343	+	127.867i	−0.0562707	+	0.282892i
$453$	−15.0668	−	22.5490i	−0.0332600	−	0.0497771i
$454$	64.3171	+	323.344i	0.141668	+	0.712211i
$455$		0			0
$456$	23.3810	−	34.9922i	0.0512742	−	0.0767372i
$457$	677.671	+	280.700i	1.48287	+	0.614224i	0.969751	−	0.244095i	$-0.0784909\pi$
$457$	677.671	+	280.700i	1.48287	+	0.614224i	0.513117	+	0.858319i	$0.328491\pi$
$458$		−	405.042i		−	0.884371i
$459$	58.4307	−	11.6534i	0.127300	−	0.0253886i
$460$		0			0
$461$	−294.134	+	710.101i	−0.638034	+	1.54035i	0.191261	+	0.981539i	$0.438742\pi$
$461$	−294.134	+	710.101i	−0.638034	+	1.54035i	−0.829295	+	0.558811i	$0.811258\pi$
$462$	2.07394	+	1.38577i	0.00448906	+	0.00299949i
$463$	138.291	+	138.291i	0.298685	+	0.298685i	0.840499	−	0.541814i	$-0.182262\pi$
$463$	138.291	+	138.291i	0.298685	+	0.298685i	−0.541814	+	0.840499i	$0.682262\pi$
$464$	−12.6599	+	2.51821i	−0.0272843	+	0.00542718i
$465$		0			0
$466$	−53.1880	−	10.5798i	−0.114137	−	0.0227033i
$467$	−311.389	+	128.982i	−0.666786	+	0.276192i	−0.690291	−	0.723532i	$-0.742517\pi$
$467$	−311.389	+	128.982i	−0.666786	+	0.276192i	0.0235049	+	0.999724i	$0.492517\pi$
$468$	−17.9608	−	43.3612i	−0.0383778	−	0.0926521i
$469$	6.38147	−	32.0818i	0.0136065	−	0.0684047i
$470$		0			0
$471$	5.52651	+	27.7837i	0.0117336	+	0.0589887i
$472$	−383.312	+	383.312i	−0.812103	+	0.812103i
$473$	−497.168	+	744.065i	−1.05110	+	1.57308i
$474$	2.19075	+	0.907438i	0.00462183	+	0.00191443i
$475$		0			0
$476$	13.3275	−	19.9678i	0.0279989	−	0.0419493i
$477$	139.451			0.292350
$478$	87.0358	−	210.123i	0.182083	−	0.439588i
$479$	−9.02462	−	6.03006i	−0.0188405	−	0.0125888i	0.546114	−	0.837711i	$-0.316106\pi$
$479$	−9.02462	−	6.03006i	−0.0188405	−	0.0125888i	−0.564955	+	0.825122i	$0.691106\pi$
$480$		0			0
$481$	62.7311	−	12.4780i	0.130418	−	0.0259418i
$482$	−286.746	+	191.598i	−0.594909	+	0.397505i
$483$	−4.83368	−	0.961478i	−0.0100076	−	0.00199064i
$484$	−523.194	+	216.714i	−1.08098	+	0.447756i
$485$		0			0
$486$	−11.2268	+	56.4408i	−0.0231003	+	0.116133i
$487$	−434.266	−	649.925i	−0.891716	−	1.33455i	−0.941930	−	0.335809i	$-0.890990\pi$
$487$	−434.266	−	649.925i	−0.891716	−	1.33455i	0.0502142	−	0.998738i	$-0.484010\pi$
$488$	−63.6478	−	319.979i	−0.130426	−	0.655694i
$489$	−9.46056	+	9.46056i	−0.0193468	+	0.0193468i
$490$		0			0
$491$	−240.667	−	99.6876i	−0.490157	−	0.203030i	0.123895	−	0.992295i	$-0.460461\pi$
$491$	−240.667	−	99.6876i	−0.490157	−	0.203030i	−0.614052	+	0.789266i	$0.710461\pi$
$492$		−	2.41378i		−	0.00490606i
$493$	−532.812	+	356.405i	−1.08076	+	0.722930i
$494$	−69.1172			−0.139913
$495$		0			0
$496$	11.5328	+	7.70594i	0.0232515	+	0.0155362i
$497$	−36.8093	−	36.8093i	−0.0740629	−	0.0740629i
$498$	16.1894	−	3.22026i	0.0325088	−	0.00646639i
$499$	132.821	−	88.7480i	0.266174	−	0.177852i	−0.415320	−	0.909675i	$-0.636330\pi$
$499$	132.821	−	88.7480i	0.266174	−	0.177852i	0.681494	+	0.731824i	$0.261330\pi$
$500$		0			0
$501$	−7.45771	+	3.08909i	−0.0148857	+	0.00616584i
$502$	−30.2903	−	73.1273i	−0.0603392	−	0.145672i
$503$	−80.4687	+	404.543i	−0.159977	+	0.804261i	0.814567	+	0.580069i	$0.196974\pi$
$503$	−80.4687	+	404.543i	−0.159977	+	0.804261i	−0.974545	+	0.224192i	$0.928026\pi$
$504$	22.2571	+	33.3100i	0.0441608	+	0.0660913i
$505$		0			0
$506$	−721.400	+	721.400i	−1.42569	+	1.42569i
$507$	−17.8486	+	26.7123i	−0.0352043	+	0.0526869i
$508$	−199.367	−	82.5803i	−0.392454	−	0.162560i
$509$			53.6570i			0.105416i	0.998610	+	0.0527082i	$0.0167853\pi$
$509$			53.6570i			0.105416i	−0.998610	+	0.0527082i	$0.983215\pi$
$510$		0			0
$511$	38.3570			0.0750626
$512$	−8.38224	+	20.2365i	−0.0163716	+	0.0395245i
$513$	−79.0986	−	52.8520i	−0.154188	−	0.103025i
$514$	325.030	+	325.030i	0.632354	+	0.632354i
$515$		0			0
$516$	19.5760	−	13.0803i	0.0379380	−	0.0253494i
$517$	1481.62	+	294.712i	2.86580	+	0.570043i
$518$	−19.4485	+	8.05583i	−0.0375454	+	0.0155518i
$519$	5.76592	+	13.9202i	0.0111097	+	0.0268211i
$520$		0			0
$521$	−30.0726	−	45.0069i	−0.0577210	−	0.0863856i	0.801486	−	0.598013i	$-0.204043\pi$
$521$	−30.0726	−	45.0069i	−0.0577210	−	0.0863856i	−0.859207	+	0.511627i	$0.829043\pi$
$522$	−80.4675	−	404.537i	−0.154152	−	0.774976i
$523$	−291.251	+	291.251i	−0.556886	+	0.556886i	−0.928419	−	0.371534i	$-0.878832\pi$
$523$	−291.251	+	291.251i	−0.556886	+	0.556886i	0.371534	+	0.928419i	$0.378832\pi$
$524$	−260.876	+	390.429i	−0.497855	+	0.745093i
$525$		0			0
$526$		−	427.055i		−	0.811892i
$527$	675.652	+	134.039i	1.28207	+	0.254344i
$528$	1.24352			0.00235515
$529$	568.967	−	1373.61i	1.07555	−	2.59661i
$530$		0			0
$531$	432.314	+	432.314i	0.814151	+	0.814151i
$532$	−37.5944	+	7.47799i	−0.0706662	+	0.0140564i
$533$	−8.54845	+	5.71189i	−0.0160384	+	0.0107165i
$534$	−24.4794	−	4.86926i	−0.0458416	−	0.00911847i
$535$		0			0
$536$	176.810	+	426.857i	0.329869	+	0.796375i
$537$	2.98625	−	15.0129i	0.00556099	−	0.0279570i
$538$	−79.2443	−	118.598i	−0.147294	−	0.220441i
$539$	176.819	+	888.930i	0.328050	+	1.64922i
$540$		0			0
$541$	70.3844	−	105.338i	0.130101	−	0.194709i	−0.760700	−	0.649103i	$-0.775144\pi$
$541$	70.3844	−	105.338i	0.130101	−	0.194709i	0.890801	+	0.454394i	$0.150144\pi$
$542$	−409.417	−	169.586i	−0.755382	−	0.312889i
$543$			4.83656i			0.00890710i
$544$	0.277465	+	547.438i	0.000510047	+	1.00632i
$545$		0			0
$546$	−0.106966	+	0.258240i	−0.000195909	+	0.000472966i
$547$	−598.290	−	399.764i	−1.09377	−	0.730831i	−0.128398	−	0.991723i	$-0.540983\pi$
$547$	−598.290	−	399.764i	−1.09377	−	0.730831i	−0.965368	+	0.260892i	$0.915983\pi$
$548$	−9.33495	−	9.33495i	−0.0170346	−	0.0170346i
$549$	−360.884	+	71.7844i	−0.657348	+	0.130755i
$550$		0			0
$551$	1003.83	+	199.674i	1.82183	+	0.362385i
$552$	64.3134	−	26.6395i	0.116510	−	0.0482599i
$553$	−2.14350	−	5.17486i	−0.00387613	−	0.00935779i
$554$	46.1248	−	231.885i	0.0832578	−	0.418565i
$555$		0			0
$556$	33.0019	+	165.912i	0.0593559	+	0.298402i
$557$	−641.617	+	641.617i	−1.15192	+	1.15192i	−0.165747	+	0.986168i	$0.553004\pi$
$557$	−641.617	+	641.617i	−1.15192	+	1.15192i	−0.986168	+	0.165747i	$0.946996\pi$
$558$	−246.237	+	368.520i	−0.441286	+	0.660430i
$559$	−92.6480	−	38.3761i	−0.165739	−	0.0686513i
$560$		0			0
$561$	57.0419	−	23.6614i	0.101679	−	0.0421772i
$562$	−460.861			−0.820037
$563$	−272.958	+	658.979i	−0.484827	+	1.17048i	0.472463	+	0.881350i	$0.343365\pi$
$563$	−272.958	+	658.979i	−0.484827	+	1.17048i	−0.957291	+	0.289127i	$0.906635\pi$
$564$	−33.0463	−	22.0808i	−0.0585927	−	0.0391504i
$565$		0			0
$566$	−290.851	+	57.8538i	−0.513871	+	0.102215i
$567$	37.4080	−	24.9953i	0.0659754	−	0.0440833i
$568$	721.154	+	143.447i	1.26964	+	0.252547i
$569$	−197.018	+	81.6076i	−0.346253	+	0.143423i	−0.549031	−	0.835802i	$-0.685003\pi$
$569$	−197.018	+	81.6076i	−0.346253	+	0.143423i	0.202778	+	0.979225i	$0.435003\pi$
$570$		0			0
$571$	−52.5107	+	263.989i	−0.0919627	+	0.462328i	0.907173	+	0.420758i	$0.138236\pi$
$571$	−52.5107	+	263.989i	−0.0919627	+	0.462328i	−0.999136	+	0.0415696i	$0.986764\pi$
$572$	−54.1671	−	81.0667i	−0.0946976	−	0.141725i
$573$	8.82817	+	44.3822i	0.0154069	+	0.0774559i
$574$	2.39270	−	2.39270i	0.00416846	−	0.00416846i
$575$		0			0
$576$	−314.095	−	130.102i	−0.545304	−	0.225872i
$577$		−	675.601i		−	1.17088i	−0.810714	−	0.585442i	$-0.800921\pi$
$577$		−	675.601i		−	1.17088i	0.810714	−	0.585442i	$-0.199079\pi$
$578$	135.318	+	325.753i	0.234114	+	0.563586i
$579$	51.8492			0.0895495
$580$		0			0
$581$	−32.4196	−	21.6621i	−0.0557997	−	0.0372842i
$582$	−26.0456	−	26.0456i	−0.0447519	−	0.0447519i
$583$	284.123	−	56.5155i	0.487346	−	0.0969391i
$584$	−450.477	+	300.999i	−0.771365	+	0.515410i
$585$		0			0
$586$	205.826	−	85.2558i	0.351238	−	0.145488i
$587$	−280.760	−	677.813i	−0.478296	−	1.15471i	−0.960408	−	0.278598i	$-0.910130\pi$
$587$	−280.760	−	677.813i	−0.478296	−	1.15471i	0.482112	−	0.876110i	$-0.339870\pi$
$588$	4.65204	−	23.3874i	0.00791163	−	0.0397744i
$589$	−611.020	−	914.457i	−1.03739	−	1.55256i
$590$		0			0
$591$	−30.1308	+	30.1308i	−0.0509828	+	0.0509828i
$592$	−5.83056	+	8.72605i	−0.00984892	+	0.0147400i
$593$	−321.567	−	133.197i	−0.542271	−	0.224616i	0.0946971	−	0.995506i	$-0.469812\pi$
$593$	−321.567	−	133.197i	−0.542271	−	0.224616i	−0.636968	+	0.770890i	$0.719812\pi$
$594$			79.6400i			0.134074i
$595$		0			0
$596$	−321.425			−0.539303
$597$	−11.1491	+	26.9163i	−0.0186752	+	0.0450860i
$598$	−95.0591	−	63.5165i	−0.158962	−	0.106215i
$599$	−150.551	−	150.551i	−0.251337	−	0.251337i	0.570182	−	0.821519i	$-0.306873\pi$
$599$	−150.551	−	150.551i	−0.251337	−	0.251337i	−0.821519	+	0.570182i	$0.806873\pi$
$600$		0			0
$601$	83.8792	−	56.0463i	0.139566	−	0.0932550i	−0.483827	−	0.875164i	$-0.660754\pi$
$601$	83.8792	−	56.0463i	0.139566	−	0.0932550i	0.623393	+	0.781909i	$0.285754\pi$
$602$	32.3710	+	6.43900i	0.0537725	+	0.0106960i
$603$	481.425	−	199.413i	0.798384	−	0.330701i
$604$	−133.514	−	322.332i	−0.221050	−	0.533662i
$605$		0			0
$606$	−10.9880	−	16.4448i	−0.0181321	−	0.0271366i
$607$	9.10189	+	45.7583i	0.0149949	+	0.0753843i	0.987558	−	0.157254i	$-0.0502642\pi$
$607$	9.10189	+	45.7583i	0.0149949	+	0.0753843i	−0.972563	+	0.232638i	$0.925264\pi$
$608$	618.062	−	618.062i	1.01655	−	1.01655i
$609$	2.29957	−	3.44155i	0.00377598	−	0.00565115i
$610$		0			0
$611$			169.285i			0.277063i
$612$	382.443	−	0.193839i	0.624907	−	0.000316730i
$613$	−772.553			−1.26028			−0.630141	−	0.776481i	$-0.717003\pi$
$613$	−772.553			−1.26028			−0.630141	+	0.776481i	$0.717003\pi$
$614$	−61.3961	+	148.223i	−0.0999936	+	0.241406i
$615$		0			0
$616$	58.8470	+	58.8470i	0.0955308	+	0.0955308i
$617$	802.584	−	159.644i	1.30078	−	0.258742i	0.504367	−	0.863490i	$-0.331726\pi$
$617$	802.584	−	159.644i	1.30078	−	0.258742i	0.796417	+	0.604747i	$0.206726\pi$
$618$	18.9796	−	12.6818i	0.0307114	−	0.0205207i
$619$	−89.8695	−	17.8761i	−0.145185	−	0.0288791i	0.121963	−	0.992535i	$-0.461081\pi$
$619$	−89.8695	−	17.8761i	−0.145185	−	0.0288791i	−0.267148	+	0.963656i	$0.586081\pi$
$620$		0			0
$621$	−60.2176	−	145.378i	−0.0969688	−	0.234103i
$622$	4.00320	−	20.1254i	0.00643601	−	0.0323560i
$623$	32.7546	+	49.0207i	0.0525756	+	0.0786850i
$624$	0.0271859	+	0.136673i	4.35672e−5	+	0.000219027i
$625$		0			0
$626$	40.4182	−	60.4901i	0.0645659	−	0.0966296i
$627$	−91.0955	−	37.7330i	−0.145288	−	0.0601802i
$628$			364.437i			0.580314i
$629$	−101.419	+	511.219i	−0.161238	+	0.812749i
$630$		0			0
$631$	231.418	−	558.693i	0.366748	−	0.885409i	−0.627530	−	0.778592i	$-0.715934\pi$
$631$	231.418	−	558.693i	0.366748	−	0.885409i	0.994279	−	0.106817i	$-0.0340659\pi$
$632$	65.7827	+	43.9546i	0.104087	+	0.0695484i
$633$	24.8721	+	24.8721i	0.0392925	+	0.0392925i
$634$	−190.285	+	37.8500i	−0.300134	+	0.0597004i
$635$		0			0
$636$	−7.47515	−	1.48690i	−0.0117534	−	0.00233789i
$637$	−93.8352	+	38.8678i	−0.147308	+	0.0610170i
$638$	−327.895	−	791.608i	−0.513942	−	1.24077i
$639$	161.784	−	813.345i	0.253184	−	1.27284i
$640$		0			0
$641$	−207.228	−	1041.80i	−0.323288	−	1.62528i	−0.710785	−	0.703410i	$-0.751660\pi$
$641$	−207.228	−	1041.80i	−0.323288	−	1.62528i	0.387496	−	0.921871i	$-0.373340\pi$
$642$	12.3223	−	12.3223i	0.0191936	−	0.0191936i
$643$	455.720	−	682.033i	0.708740	−	1.06070i	−0.285996	−	0.958231i	$-0.592324\pi$
$643$	455.720	−	682.033i	0.708740	−	1.06070i	0.994736	−	0.102473i	$-0.0326757\pi$
$644$	−58.5769	−	24.2633i	−0.0909579	−	0.0376760i
$645$		0			0
$646$	215.266	−	520.443i	0.333228	−	0.805639i
$647$	−351.542			−0.543342			−0.271671	−	0.962390i	$-0.587576\pi$
$647$	−351.542			−0.543342			−0.271671	+	0.962390i	$0.587576\pi$
$648$	−243.187	+	587.105i	−0.375289	+	0.906027i
$649$	1056.02	+	705.609i	1.62715	+	1.08722i
$650$		0			0
$651$	−4.36227	+	0.867708i	−0.00670087	+	0.00133289i
$652$	−143.115	+	95.6264i	−0.219502	+	0.146666i
$653$	523.249	+	104.081i	0.801300	+	0.159389i	0.578721	−	0.815526i	$-0.303552\pi$
$653$	523.249	+	104.081i	0.801300	+	0.159389i	0.222580	+	0.974914i	$0.428552\pi$
$654$	10.1737	−	4.21410i	0.0155562	−	0.00644357i
$655$		0			0
$656$	0.329109	−	1.65454i	0.000501690	−	0.00252217i
$657$	339.479	+	508.066i	0.516710	+	0.773311i
$658$	−10.8697	−	54.6455i	−0.0165193	−	0.0830479i
$659$	541.088	−	541.088i	0.821075	−	0.821075i	−0.165187	−	0.986262i	$-0.552823\pi$
$659$	541.088	−	541.088i	0.821075	−	0.821075i	0.986262	+	0.165187i	$0.0528229\pi$
$660$		0			0
$661$	−297.311	−	123.150i	−0.449790	−	0.186309i	0.146277	−	0.989244i	$-0.453271\pi$
$661$	−297.311	−	123.150i	−0.449790	−	0.186309i	−0.596067	+	0.802935i	$0.703271\pi$
$662$		−	485.764i		−	0.733782i
$663$	3.84764	+	5.75209i	0.00580338	+	0.00867585i
$664$	550.737			0.829423
$665$		0			0
$666$	−278.834	−	186.311i	−0.418670	−	0.279746i
$667$	1197.11	+	1197.11i	1.79476	+	1.79476i
$668$	−101.852	+	20.2597i	−0.152474	+	0.0303289i
$669$	−45.0361	+	30.0922i	−0.0673186	+	0.0449808i
$670$		0			0
$671$	−706.187	+	292.512i	−1.05244	+	0.435935i
$672$	−1.35272	−	3.26576i	−0.00201298	−	0.00485976i
$673$	−112.955	+	567.862i	−0.167838	+	0.843778i	0.801490	+	0.598008i	$0.204041\pi$
$673$	−112.955	+	567.862i	−0.167838	+	0.843778i	−0.969328	+	0.245770i	$0.920959\pi$
$674$	23.5513	+	35.2469i	0.0349425	+	0.0522952i
$675$		0			0
$676$	−292.251	+	292.251i	−0.432324	+	0.432324i
$677$	−710.298	+	1063.04i	−1.04918	+	1.57022i	−0.250827	+	0.968032i	$0.580702\pi$
$677$	−710.298	+	1063.04i	−1.04918	+	1.57022i	−0.798358	+	0.602183i	$0.794298\pi$
$678$	11.4275	+	4.73342i	0.0168547	+	0.00698144i
$679$			87.0074i			0.128140i
$680$		0			0
$681$	−52.7039			−0.0773919
$682$	−352.342	+	850.630i	−0.516631	+	1.24726i
$683$	−479.115	−	320.134i	−0.701485	−	0.468718i	0.152978	−	0.988230i	$-0.451114\pi$
$683$	−479.115	−	320.134i	−0.701485	−	0.468718i	−0.854463	+	0.519512i	$0.826114\pi$
$684$	−431.781	−	431.781i	−0.631258	−	0.631258i
$685$		0			0
$686$	55.7696	−	37.2641i	0.0812968	−	0.0543208i
$687$	63.5076	+	12.6325i	0.0924419	+	0.0183878i
$688$	15.2019	−	6.29684i	0.0220958	−	0.00915239i
$689$	12.4230	+	29.9919i	0.0180305	+	0.0435296i
$690$		0			0
$691$	424.826	+	635.797i	0.614799	+	0.920111i	0.999996	−	0.00272293i	$-0.000866737\pi$
$691$	424.826	+	635.797i	0.614799	+	0.920111i	−0.385198	+	0.922834i	$0.625867\pi$
$692$	37.8157	+	190.112i	0.0546470	+	0.274729i
$693$	66.3698	−	66.3698i	0.0957718	−	0.0957718i
$694$	299.532	−	448.282i	0.431603	−	0.645939i
$695$		0			0
$696$			58.4642i			0.0840003i
$697$	−16.3856	−	82.1584i	−0.0235088	−	0.117874i
$698$	−97.3770			−0.139509
$699$	3.31766	−	8.00953i	0.00474629	−	0.0114586i
$700$		0			0
$701$	−146.918	−	146.918i	−0.209583	−	0.209583i	0.594507	−	0.804090i	$-0.297347\pi$
$701$	−146.918	−	146.918i	−0.209583	−	0.209583i	−0.804090	+	0.594507i	$0.797347\pi$
$702$	−8.75310	+	1.74110i	−0.0124688	+	0.00248020i
$703$	691.907	−	462.317i	0.984220	−	0.657635i
$704$	−692.675	−	137.782i	−0.983914	−	0.195713i
$705$		0			0
$706$	105.507	+	254.716i	0.149443	+	0.360787i
$707$	−9.11429	+	45.8207i	−0.0128915	+	0.0648100i
$708$	−18.5643	−	27.7834i	−0.0262207	−	0.0392421i
$709$	84.7644	+	426.139i	0.119555	+	0.601043i	0.993387	+	0.114815i	$0.0366275\pi$
$709$	84.7644	+	426.139i	0.119555	+	0.601043i	−0.873832	+	0.486228i	$0.838373\pi$
$710$		0			0
$711$	49.5737	−	74.1922i	0.0697239	−	0.104349i
$712$	−769.362	−	318.680i	−1.08056	−	0.447585i
$713$		−	1819.19i		−	2.55146i
$714$	−1.61136	−	1.60973i	−0.00225681	−	0.00225452i
$715$		0			0
$716$	75.3594	−	181.934i	0.105251	−	0.254097i
$717$	30.2313	+	20.1999i	0.0421636	+	0.0281728i
$718$	136.163	+	136.163i	0.189642	+	0.189642i
$719$	623.179	−	123.958i	0.866730	−	0.172403i	0.258352	−	0.966051i	$-0.416820\pi$
$719$	623.179	−	123.958i	0.866730	−	0.172403i	0.608378	+	0.793647i	$0.291820\pi$
$720$		0			0
$721$	−52.8837	−	10.5192i	−0.0733477	−	0.0145898i
$722$	−423.714	+	175.508i	−0.586862	+	0.243086i
$723$	−21.0981	−	50.9352i	−0.0291813	−	0.0704498i
$724$	−12.1389	+	61.0263i	−0.0167664	+	0.0842905i
$725$		0			0
$726$	10.4817	+	52.6953i	0.0144377	+	0.0725830i
$727$	158.734	−	158.734i	0.218341	−	0.218341i	−0.589458	−	0.807799i	$-0.700659\pi$
$727$	158.734	−	158.734i	0.218341	−	0.218341i	0.807799	+	0.589458i	$0.200659\pi$
$728$	−5.18125	+	7.75429i	−0.00711710	+	0.0106515i
$729$	656.473	+	271.920i	0.900512	+	0.373004i
$730$		0			0
$731$	577.519	−	578.105i	0.790040	−	0.790841i
$732$	20.1103			0.0274731
$733$	223.658	−	539.959i	0.305127	−	0.736643i	−0.694722	−	0.719278i	$-0.744473\pi$
$733$	223.658	−	539.959i	0.305127	−	0.736643i	0.999849	−	0.0173642i	$-0.00552747\pi$
$734$	704.641	+	470.826i	0.960002	+	0.641453i
$735$		0			0
$736$	1418.02	−	282.062i	1.92666	−	0.383236i
$737$	900.057	−	601.399i	1.22124	−	0.816010i
$738$	52.8695	+	10.5164i	0.0716389	+	0.0142499i
$739$	394.314	−	163.330i	0.533577	−	0.221015i	−0.0995919	−	0.995028i	$-0.531754\pi$
$739$	394.314	−	163.330i	0.533577	−	0.221015i	0.633169	+	0.774013i	$0.281754\pi$
$740$		0			0
$741$	2.15563	−	10.8371i	0.00290908	−	0.0146249i
$742$	−5.93593	−	8.88375i	−0.00799991	−	0.0119727i
$743$	124.034	+	623.559i	0.166936	+	0.839244i	0.969954	+	0.243289i	$0.0782264\pi$
$743$	124.034	+	623.559i	0.166936	+	0.839244i	−0.803018	+	0.595955i	$0.796774\pi$
$744$	44.4227	−	44.4227i	0.0597080	−	0.0597080i
$745$		0			0
$746$	89.3986	+	37.0301i	0.119837	+	0.0496382i
$747$		−	621.142i		−	0.831515i
$748$	779.125	−	155.388i	1.04161	−	0.207738i
$749$	−41.1636			−0.0549580
$750$		0			0
$751$	−537.116	−	358.890i	−0.715202	−	0.477883i	0.143962	−	0.989583i	$-0.454016\pi$
$751$	−537.116	−	358.890i	−0.715202	−	0.477883i	−0.859164	+	0.511701i	$0.829016\pi$
$752$	−19.6411	−	19.6411i	−0.0261185	−	0.0261185i
$753$	12.4105	−	2.46861i	0.0164814	−	0.00327836i
$754$	79.8359	−	53.3446i	0.105883	−	0.0707488i
$755$		0			0
$756$	−4.57263	+	1.89405i	−0.00604846	+	0.00250535i
$757$	398.561	+	962.210i	0.526500	+	1.27108i	0.933802	+	0.357790i	$0.116470\pi$
$757$	398.561	+	962.210i	0.526500	+	1.27108i	−0.407302	+	0.913293i	$0.633530\pi$
$758$	100.684	−	506.173i	0.132829	−	0.667775i
$759$	−90.6112	−	135.609i	−0.119382	−	0.178668i
$760$		0			0
$761$	501.407	−	501.407i	0.658880	−	0.658880i	−0.296235	−	0.955115i	$-0.595731\pi$
$761$	501.407	−	501.407i	0.658880	−	0.658880i	0.955115	+	0.296235i	$0.0957313\pi$
$762$	−11.3743	+	17.0229i	−0.0149270	+	0.0223398i
$763$	−24.0318	−	9.95430i	−0.0314965	−	0.0130463i
$764$			582.160i			0.761989i
$765$		0			0
$766$	−513.121			−0.669870
$767$	−54.4655	+	131.491i	−0.0710110	+	0.171436i
$768$	40.9566	+	27.3663i	0.0533289	+	0.0356332i
$769$	−733.316	−	733.316i	−0.953597	−	0.953597i	0.0453730	−	0.998970i	$-0.485552\pi$
$769$	−733.316	−	733.316i	−0.953597	−	0.953597i	−0.998970	+	0.0453730i	$0.985552\pi$
$770$		0			0
$771$	−61.0993	+	40.8253i	−0.0792469	+	0.0529511i
$772$	654.218	+	130.132i	0.847433	+	0.168565i
$773$	−97.4479	+	40.3642i	−0.126065	+	0.0522177i	−0.444824	−	0.895618i	$-0.646734\pi$
$773$	−97.4479	+	40.3642i	−0.126065	+	0.0522177i	0.318759	+	0.947836i	$0.396734\pi$
$774$	201.211	+	485.765i	0.259962	+	0.627604i
$775$		0			0
$776$	−682.774	−	1021.84i	−0.879863	−	1.31681i
$777$	−0.656536	−	3.30063i	−0.000844962	−	0.00424791i
$778$	−7.86134	+	7.86134i	−0.0101045	+	0.0101045i
$779$	−74.3143	+	111.219i	−0.0953970	+	0.142772i
$780$		0			0
$781$		−	1722.71i		−	2.20577i
$782$	774.332	−	517.960i	0.990195	−	0.662353i
$783$	132.156			0.168782
$784$	6.37753	−	15.3967i	0.00813460	−	0.0196387i
$785$		0			0
$786$	31.5015	+	31.5015i	0.0400782	+	0.0400782i
$787$	−21.3677	+	4.25029i	−0.0271508	+	0.00540063i	−0.208647	−	0.977991i	$-0.566906\pi$
$787$	−21.3677	+	4.25029i	−0.0271508	+	0.00540063i	0.181496	+	0.983392i	$0.441906\pi$
$788$	−455.806	+	304.560i	−0.578434	+	0.386497i
$789$	66.9591	+	13.3190i	0.0848658	+	0.0168809i
$790$		0			0
$791$	−11.1810	−	26.9933i	−0.0141353	−	0.0341256i
$792$	−258.645	+	1300.29i	−0.326571	+	1.64179i
$793$	−47.5883	−	71.2209i	−0.0600104	−	0.0898120i
$794$	−162.488	−	816.883i	−0.204645	−	1.02882i
$795$		0			0
$796$	−208.231	+	311.640i	−0.261597	+	0.391508i
$797$	−1241.09	−	514.075i	−1.55720	−	0.645012i	−0.572598	−	0.819836i	$-0.694064\pi$
$797$	−1241.09	−	514.075i	−1.55720	−	0.645012i	−0.984600	+	0.174824i	$0.944064\pi$
$798$			3.63663i			0.00455719i
$799$	−1274.69	−	527.239i	−1.59536	−	0.659874i
$800$		0			0
$801$	−359.420	+	867.716i	−0.448714	+	1.08329i
$802$	−38.0322	−	25.4123i	−0.0474217	−	0.0316861i
$803$	897.571	+	897.571i	1.11777	+	1.11777i
$804$	−27.9326	+	5.55614i	−0.0347421	+	0.00691063i
$805$		0			0
$806$	−101.194	−	20.1288i	−0.125551	−	0.0249737i
$807$	21.0667	−	8.72611i	0.0261050	−	0.0108130i
$808$	−252.528	−	609.656i	−0.312534	−	0.754525i
$809$	183.354	−	921.783i	0.226643	−	1.13941i	−0.685037	−	0.728508i	$-0.740214\pi$
$809$	183.354	−	921.783i	0.226643	−	1.13941i	0.911680	−	0.410902i	$-0.134786\pi$
$810$		0			0
$811$	−135.432	−	680.861i	−0.166993	−	0.839533i	−0.969914	−	0.243447i	$-0.921722\pi$
$811$	−135.432	−	680.861i	−0.166993	−	0.839533i	0.802921	−	0.596086i	$-0.203278\pi$
$812$	37.6530	−	37.6530i	0.0463707	−	0.0463707i
$813$	39.3587	−	58.9045i	0.0484117	−	0.0724533i
$814$	−643.613	−	266.593i	−0.790680	−	0.327510i
$815$		0			0
$816$	−1.11380	−	0.220961i	−0.00136495	−	0.000270786i
$817$	−1304.71			−1.59695
$818$	134.177	−	323.931i	0.164030	−	0.396004i
$819$	8.74558	+	5.84361i	0.0106784	+	0.00713506i
$820$		0			0
$821$	37.4333	−	7.44594i	0.0455947	−	0.00906936i	−0.172240	−	0.985055i	$-0.555101\pi$
$821$	37.4333	−	7.44594i	0.0455947	−	0.00906936i	0.217835	+	0.975986i	$0.430101\pi$
$822$	−1.04141	+	0.695851i	−0.00126693	+	0.000846534i
$823$	−428.003	−	85.1351i	−0.520052	−	0.103445i	−0.0719169	−	0.997411i	$-0.522912\pi$
$823$	−428.003	−	85.1351i	−0.520052	−	0.103445i	−0.448135	+	0.893966i	$0.647912\pi$
$824$	703.631	−	291.454i	0.853921	−	0.353706i
$825$		0			0
$826$	9.13859	−	45.9428i	0.0110637	−	0.0556208i
$827$	423.131	+	633.260i	0.511645	+	0.765731i	0.993898	−	0.110301i	$-0.0351814\pi$
$827$	423.131	+	633.260i	0.511645	+	0.765731i	−0.482253	+	0.876032i	$0.660181\pi$
$828$	−197.050	−	990.635i	−0.237982	−	1.19642i
$829$	−625.296	+	625.296i	−0.754278	+	0.754278i	−0.975275	−	0.220997i	$-0.929069\pi$
$829$	−625.296	+	625.296i	−0.754278	+	0.754278i	0.220997	+	0.975275i	$0.429069\pi$
$830$		0			0
$831$	34.9193	+	14.4641i	0.0420209	+	0.0174056i
$832$		−	79.1430i		−	0.0951238i
$833$	−0.419473	−	827.620i	−0.000503570	−	0.993541i
$834$	16.0492			0.0192436
$835$		0			0
$836$	−1054.71	−	704.737i	−1.26162	−	0.842987i
$837$	−100.416	−	100.416i	−0.119971	−	0.119971i
$838$	478.893	−	95.2578i	0.571472	−	0.113673i
$839$	222.326	−	148.554i	0.264990	−	0.177060i	−0.415976	−	0.909375i	$-0.636560\pi$
$839$	222.326	−	148.554i	0.264990	−	0.177060i	0.680966	+	0.732315i	$0.261560\pi$
$840$		0			0
$841$	−536.631	+	222.280i	−0.638087	+	0.264304i
$842$	238.911	+	576.783i	0.283743	+	0.685015i
$843$	14.3733	−	72.2597i	0.0170502	−	0.0857173i
$844$	251.405	+	376.254i	0.297873	+	0.445799i
$845$		0			0
$846$	627.617	−	627.617i	0.741863	−	0.741863i
$847$	70.5087	−	105.524i	0.0832452	−	0.124585i
$848$	−4.92115	−	2.03841i	−0.00580324	−	0.00240378i
$849$		−	47.4077i		−	0.0558394i
$850$		0			0
$851$	1376.46			1.61746
$852$	−17.3446	+	41.8736i	−0.0203575	+	0.0491474i
$853$	−86.3136	−	57.6729i	−0.101188	−	0.0676119i	0.503947	−	0.863735i	$-0.331881\pi$
$853$	−86.3136	−	57.6729i	−0.101188	−	0.0676119i	−0.605135	+	0.796123i	$0.706881\pi$
$854$	19.9346	+	19.9346i	0.0233426	+	0.0233426i
$855$		0			0
$856$	483.439	−	323.024i	0.564765	−	0.377364i
$857$	628.513	+	125.019i	0.733387	+	0.145880i	0.547636	−	0.836717i	$-0.315528\pi$
$857$	628.513	+	125.019i	0.733387	+	0.145880i	0.185752	+	0.982597i	$0.440528\pi$
$858$	−8.54598	+	3.53986i	−0.00996035	+	0.00412571i
$859$	−32.2425	−	77.8402i	−0.0375349	−	0.0906173i	0.904000	−	0.427532i	$-0.140617\pi$
$859$	−32.2425	−	77.8402i	−0.0375349	−	0.0906173i	−0.941535	+	0.336914i	$0.890617\pi$
$860$		0			0
$861$	0.300534	+	0.449781i	0.000349052	+	0.000522394i
$862$	−136.683	−	687.152i	−0.158565	−	0.797160i
$863$	−681.756	+	681.756i	−0.789984	+	0.789984i	−0.981491	−	0.191507i	$-0.938663\pi$
$863$	−681.756	+	681.756i	−0.789984	+	0.789984i	0.191507	+	0.981491i	$0.438663\pi$
$864$	62.7029	−	93.8415i	0.0725728	−	0.108613i
$865$		0			0
$866$			236.044i			0.272568i
$867$	−55.2959	+	11.0573i	−0.0637785	+	0.0127536i
$868$	−57.2196			−0.0659212
$869$	70.9352	−	171.253i	0.0816286	−	0.197069i
$870$		0			0
$871$	85.7759	+	85.7759i	0.0984798	+	0.0984798i
$872$	360.352	−	71.6785i	0.413248	−	0.0822001i
$873$	−1152.47	+	770.059i	−1.32013	+	0.882083i
$874$	−1458.86	−	290.185i	−1.66918	−	0.332020i
$875$		0			0
$876$	−12.7802	−	30.8541i	−0.0145893	−	0.0352216i
$877$	2.51060	−	12.6217i	0.00286272	−	0.0143919i	−0.979328	−	0.202281i	$-0.935165\pi$
$877$	2.51060	−	12.6217i	0.00286272	−	0.0143919i	0.982190	+	0.187889i	$0.0601646\pi$
$878$	150.695	+	225.530i	0.171634	+	0.256868i
$879$	6.94819	+	34.9309i	0.00790466	+	0.0397394i
$880$		0			0
$881$	−440.855	+	659.786i	−0.500403	+	0.748906i	−0.992581	−	0.121589i	$-0.961201\pi$
$881$	−440.855	+	659.786i	−0.500403	+	0.748906i	0.492178	+	0.870495i	$0.336201\pi$
$882$	491.990	+	203.789i	0.557811	+	0.231053i
$883$		−	338.313i		−	0.383140i	−0.981479	−	0.191570i	$-0.938642\pi$
$883$		−	338.313i		−	0.383140i	0.981479	−	0.191570i	$-0.0613580\pi$
$884$	34.1118	+	82.2352i	0.0385880	+	0.0930262i
$885$		0			0
$886$	−118.159	+	285.261i	−0.133362	+	0.321965i
$887$	−1243.11	−	830.619i	−1.40148	−	0.936436i	−0.999787	−	0.0206596i	$-0.993423\pi$
$887$	−1243.11	−	830.619i	−1.40148	−	0.936436i	−0.401689	−	0.915776i	$-0.631577\pi$
$888$	33.6116	+	33.6116i	0.0378509	+	0.0378509i
$889$	47.4315	−	9.43472i	0.0533538	−	0.0106127i
$890$		0			0
$891$	1460.26	+	290.465i	1.63891	+	0.325999i
$892$	−643.779	+	266.662i	−0.721726	+	0.298948i
$893$	842.851	+	2034.82i	0.943842	+	2.27864i
$894$	−5.94929	+	29.9091i	−0.00665469	+	0.0334554i
$895$		0			0
$896$	−9.05521	−	45.5236i	−0.0101063	−	0.0508076i
$897$	12.9236	−	12.9236i	0.0144076	−	0.0144076i
$898$	−209.420	+	313.419i	−0.233207	+	0.349019i
$899$	1411.55	+	584.685i	1.57014	+	0.650373i
$900$		0			0
$901$	−264.526	+	0.134073i	−0.293592	+	0.000148805i
$902$	111.980			0.124147
$903$	−2.01918	+	4.87472i	−0.00223608	+	0.00539836i
$904$	343.139	+	229.278i	0.379578	+	0.253626i
$905$		0			0
$906$	−32.4648	+	6.45765i	−0.0358331	+	0.00712764i
$907$	−505.610	+	337.838i	−0.557453	+	0.372478i	−0.802151	−	0.597121i	$-0.796311\pi$
$907$	−505.610	+	337.838i	−0.557453	+	0.372478i	0.244698	+	0.969599i	$0.421311\pi$
$908$	−665.003	−	132.277i	−0.732382	−	0.145680i
$909$	−687.593	+	284.810i	−0.756428	+	0.313323i
$910$		0			0
$911$	−35.8895	+	180.429i	−0.0393957	+	0.198056i	−0.995471	−	0.0950656i	$-0.969694\pi$
$911$	−35.8895	+	180.429i	−0.0393957	+	0.198056i	0.956075	+	0.293121i	$0.0946939\pi$
$912$	1.00725	+	1.50746i	0.00110445	+	0.00165292i
$913$	−251.731	−	1265.54i	−0.275718	−	1.38613i
$914$	633.061	−	633.061i	0.692627	−	0.692627i
$915$		0			0
$916$	769.616	+	318.786i	0.840192	+	0.348019i
$917$		−	105.233i		−	0.114758i
$918$	14.1513	−	71.3323i	0.0154153	−	0.0777040i
$919$	99.8948			0.108699			0.0543497	−	0.998522i	$-0.482691\pi$
$919$	99.8948			0.108699			0.0543497	+	0.998522i	$0.482691\pi$
$920$		0			0
$921$	−21.3255	−	14.2492i	−0.0231547	−	0.0154715i
$922$	663.357	+	663.357i	0.719476	+	0.719476i
$923$	189.340	−	37.6620i	0.205135	−	0.0408039i
$924$	−4.26537	+	2.85003i	−0.00461620	+	0.00308444i
$925$		0			0
$926$	220.537	−	91.3494i	0.238161	−	0.0986495i
$927$	−328.712	−	793.582i	−0.354598	−	0.856075i
$928$	−236.891	+	1190.93i	−0.255270	+	1.28333i
$929$	200.330	+	299.815i	0.215641	+	0.322729i	0.923482	−	0.383643i	$-0.125331\pi$
$929$	200.330	+	299.815i	0.215641	+	0.322729i	−0.707841	+	0.706372i	$0.750331\pi$
$930$		0			0
$931$	−934.388	+	934.388i	−1.00364	+	1.00364i
$932$	61.9637	−	92.7353i	0.0664847	−	0.0995014i
$933$	3.03067	+	1.25535i	0.00324831	+	0.00134549i
$934$			411.382i			0.440452i
$935$		0			0
$936$	−148.568			−0.158726
$937$	−495.480	+	1196.19i	−0.528794	+	1.27662i	0.403520	+	0.914971i	$0.367786\pi$
$937$	−495.480	+	1196.19i	−0.528794	+	1.27662i	−0.932314	+	0.361650i	$0.882214\pi$
$938$	−33.1962	−	22.1810i	−0.0353904	−	0.0236471i
$939$	8.22385	+	8.22385i	0.00875809	+	0.00875809i
$940$		0			0
$941$	−439.777	+	293.850i	−0.467351	+	0.312274i	−0.766854	−	0.641821i	$-0.778179\pi$
$941$	−439.777	+	293.850i	−0.467351	+	0.312274i	0.299503	+	0.954095i	$0.403179\pi$
$942$	33.9115	+	6.74541i	0.0359995	+	0.00716074i
$943$	−204.414	+	84.6709i	−0.216770	+	0.0897889i
$944$	−8.93683	−	21.5754i	−0.00946698	−	0.0228553i
$945$		0			0
$946$	606.821	+	908.172i	0.641460	+	0.960012i
$947$	−57.3169	−	288.151i	−0.0605247	−	0.304278i	0.938651	−	0.344868i	$-0.112076\pi$
$947$	−57.3169	−	288.151i	−0.0605247	−	0.304278i	−0.999176	+	0.0405898i	$0.987076\pi$
$948$	−3.44843	+	3.44843i	−0.00363758	+	0.00363758i
$949$	−79.0277	+	118.273i	−0.0832747	+	0.124629i
$950$		0			0
$951$		−	31.0158i		−	0.0326138i
$952$	−42.2517	−	63.1649i	−0.0443821	−	0.0663496i
$953$	315.219			0.330765			0.165383	−	0.986229i	$-0.447114\pi$
$953$	315.219			0.330765			0.165383	+	0.986229i	$0.447114\pi$
$954$	65.1356	−	157.251i	0.0682763	−	0.164834i
$955$		0			0
$956$	330.752	+	330.752i	0.345975	+	0.345975i
$957$	134.345	−	26.7228i	0.140381	−	0.0279236i
$958$	−11.0150	+	7.36001i	−0.0114980	+	0.00768269i
$959$	2.90173	+	0.577191i	0.00302579	+	0.000601867i
$960$		0			0
$961$	−260.520	−	628.950i	−0.271092	−	0.654474i
$962$	15.2301	−	76.5668i	0.0158317	−	0.0795912i
$963$	−364.318	−	545.241i	−0.378316	−	0.566190i
$964$	−138.371	−	695.639i	−0.143539	−	0.721617i
$965$		0			0
$966$	−3.34195	+	5.00158i	−0.00345958	+	0.00517762i
$967$	−288.329	−	119.430i	−0.298169	−	0.123506i	0.228584	−	0.973524i	$-0.426591\pi$
$967$	−288.329	−	119.430i	−0.298169	−	0.123506i	−0.526753	+	0.850019i	$0.676591\pi$
$968$			1792.61i			1.85187i
$969$	74.8880	+	49.9837i	0.0772838	+	0.0515827i
$970$		0			0
$971$	344.439	−	831.550i	0.354726	−	0.856385i	−0.641297	−	0.767293i	$-0.721603\pi$
$971$	344.439	−	831.550i	0.354726	−	0.856385i	0.996023	−	0.0890923i	$-0.0283966\pi$
$972$	−98.4066	−	65.7532i	−0.101241	−	0.0676473i
$973$	−26.8068	−	26.8068i	−0.0275506	−	0.0275506i
$974$	−935.724	+	186.127i	−0.960702	+	0.191096i
$975$		0			0
$976$	13.7847	+	2.74195i	0.0141237	+	0.00280937i
$977$	1198.58	−	496.470i	1.22680	−	0.508158i	0.327235	−	0.944943i	$-0.393883\pi$
$977$	1198.58	−	496.470i	1.22680	−	0.508158i	0.899566	+	0.436785i	$0.143883\pi$
$978$	6.24926	+	15.0871i	0.00638984	+	0.0154264i
$979$	−380.635	+	1913.58i	−0.388799	+	1.95463i
$980$		0			0
$981$	−80.8417	−	406.419i	−0.0824075	−	0.414290i
$982$	−224.825	+	224.825i	−0.228946	+	0.228946i
$983$	365.673	−	547.268i	0.371997	−	0.556732i	−0.597490	−	0.801876i	$-0.703835\pi$
$983$	365.673	−	547.268i	0.371997	−	0.556732i	0.969487	+	0.245144i	$0.0788352\pi$
$984$	−7.05914	−	2.92399i	−0.00717393	−	0.00297154i
$985$		0			0
$986$	153.029	+	767.295i	0.155202	+	0.778190i
$987$	8.90702			0.00902434
$988$	54.3982	−	131.329i	0.0550589	−	0.132924i
$989$	−1794.41	−	1198.98i	−1.81436	−	1.21232i
$990$		0			0
$991$	−564.247	+	112.236i	−0.569371	+	0.113255i	−0.471377	−	0.881932i	$-0.656243\pi$
$991$	−564.247	+	112.236i	−0.569371	+	0.113255i	−0.0979944	+	0.995187i	$0.531243\pi$
$992$	1084.90	−	724.906i	1.09365	−	0.730752i
$993$	76.1643	+	15.1500i	0.0767012	+	0.0152568i
$994$	−58.7009	+	24.3147i	−0.0590553	+	0.0244615i
$995$		0			0
$996$	−6.62294	+	33.2957i	−0.00664953	+	0.0334295i
$997$	−284.665	−	426.031i	−0.285521	−	0.427313i	0.660789	−	0.750571i	$-0.270222\pi$
$997$	−284.665	−	426.031i	−0.285521	−	0.427313i	−0.946311	+	0.323259i	$0.895222\pi$
$998$	−38.0376	−	191.228i	−0.0381138	−	0.191611i
$999$	75.9780	−	75.9780i	0.0760541	−	0.0760541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.d.401.8	yes	96
5.2	odd	4		425.3.t.f.299.8		96
5.3	odd	4		425.3.t.g.299.5		96
5.4	even	2		425.3.u.c.401.5	yes	96
17.12	odd	16	inner	425.3.u.d.301.8	yes	96
85.12	even	16		425.3.t.g.199.5		96
85.29	odd	16		425.3.u.c.301.5	✓	96
85.63	even	16		425.3.t.f.199.8		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.3.t.f.199.8		96	85.63	even	16
425.3.t.f.299.8		96	5.2	odd	4
425.3.t.g.199.5		96	85.12	even	16
425.3.t.g.299.5		96	5.3	odd	4
425.3.u.c.301.5	✓	96	85.29	odd	16
425.3.u.c.401.5	yes	96	5.4	even	2
425.3.u.d.301.8	yes	96	17.12	odd	16	inner
425.3.u.d.401.8	yes	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.467086 - 1.12765i) q^{2} +(0.162239 + 0.108405i) q^{3} +(1.77501 + 1.77501i) q^{4} +(0.198022 - 0.132314i) q^{6} +(-0.551755 - 0.109751i) q^{7} +(7.34125 - 3.04085i) q^{8} +(-3.42958 - 8.27974i) q^{9} +(-10.3431 - 15.4795i) q^{11} +(0.0955567 + 0.480396i) q^{12} +(1.47521 - 1.47521i) q^{13} +(-0.381477 + 0.570921i) q^{14} +0.342319i q^{16} +(6.51358 + 15.7027i) q^{17} -10.9385 q^{18} +(10.3872 - 25.0770i) q^{19} +(-0.0776188 - 0.0776188i) q^{21} +(-22.2866 + 4.43307i) q^{22} +(37.3309 - 24.9437i) q^{23} +(1.52068 + 0.302482i) q^{24} +(-0.974463 - 2.35256i) q^{26} +(0.683751 - 3.43745i) q^{27} +(-0.784563 - 1.17418i) q^{28} +(7.35634 + 36.9828i) q^{29} +(22.5110 - 33.6901i) q^{31} +(29.7510 + 12.3233i) q^{32} -3.63263i q^{33} +(20.7494 - 0.0105167i) q^{34} +(8.60909 - 20.7842i) q^{36} +(25.4910 + 17.0326i) q^{37} +(-23.4262 - 23.4262i) q^{38} +(0.399256 - 0.0794170i) q^{39} +(-4.83333 - 0.961410i) q^{41} +(-0.123781 + 0.0512718i) q^{42} +(-18.3947 - 44.4087i) q^{43} +(9.11725 - 45.8355i) q^{44} +(-10.6909 - 53.7469i) q^{46} +(-57.3767 + 57.3767i) q^{47} +(-0.0371090 + 0.0555375i) q^{48} +(-44.9777 - 18.6304i) q^{49} +(-0.645485 + 3.25369i) q^{51} +5.23702 q^{52} +(-5.95470 + 14.3759i) q^{53} +(-3.55685 - 2.37661i) q^{54} +(-4.38431 + 0.872094i) q^{56} +(4.40368 - 2.94245i) q^{57} +(45.1396 + 8.97882i) q^{58} +(-63.0273 + 26.1068i) q^{59} +(8.00992 - 40.2686i) q^{61} +(-27.4759 - 41.1206i) q^{62} +(0.983580 + 4.94479i) q^{63} +(26.8243 - 26.8243i) q^{64} +(-4.09632 - 1.69675i) q^{66} +58.1450i q^{67} +(-16.3107 + 39.4341i) q^{68} +8.76055 q^{69} +(76.9389 + 51.4089i) q^{71} +(-50.3548 - 50.3548i) q^{72} +(-66.8722 + 13.3017i) q^{73} +(31.1132 - 20.7892i) q^{74} +(62.9495 - 26.0745i) q^{76} +(4.00797 + 9.67608i) q^{77} +(0.0969328 - 0.487314i) q^{78} +(5.53158 + 8.27860i) q^{79} +(-56.5498 + 56.5498i) q^{81} +(-3.34171 + 5.00123i) q^{82} +(64.0331 + 26.5234i) q^{83} -0.275549i q^{84} -58.6692 q^{86} +(-2.81563 + 6.79752i) q^{87} +(-123.002 - 82.1874i) q^{88} +(-74.1047 - 74.1047i) q^{89} +(-0.975860 + 0.652049i) q^{91} +(110.538 + 21.9874i) q^{92} +(7.30434 - 3.02556i) q^{93} +(37.9007 + 91.5005i) q^{94} +(3.49088 + 5.22447i) q^{96} +(-30.1730 - 151.690i) q^{97} +(-42.0169 + 42.0169i) q^{98} +(-92.6941 + 138.726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{12} + 24 q^{13} + 32 q^{14} - 8 q^{17} - 64 q^{18} - 24 q^{19} - 96 q^{22} - 56 q^{23} - 336 q^{24} - 224 q^{26} + 144 q^{27} - 480 q^{28} - 64 q^{31} + 40 q^{32} + 64 q^{34} + 192 q^{36} - 128 q^{37}+ \cdots - 160 q^{99}+O(q^{100}) \) 96 * q + 96 * q^12 + 24 * q^13 + 32 * q^14 - 8 * q^17 - 64 * q^18 - 24 * q^19 - 96 * q^22 - 56 * q^23 - 336 * q^24 - 224 * q^26 + 144 * q^27 - 480 * q^28 - 64 * q^31 + 40 * q^32 + 64 * q^34 + 192 * q^36 - 128 * q^37 + 496 * q^38 + 16 * q^39 + 216 * q^41 - 432 * q^42 + 592 * q^43 - 32 * q^44 + 336 * q^46 + 160 * q^48 - 32 * q^49 - 32 * q^51 - 96 * q^53 + 584 * q^54 - 40 * q^56 - 1120 * q^57 - 256 * q^58 + 544 * q^59 + 112 * q^61 - 560 * q^62 - 312 * q^63 + 592 * q^64 - 24 * q^66 - 192 * q^69 - 336 * q^71 + 1040 * q^72 - 336 * q^74 - 1016 * q^76 + 960 * q^77 - 384 * q^79 - 928 * q^81 + 1200 * q^82 + 144 * q^83 + 64 * q^86 + 672 * q^87 + 832 * q^88 + 576 * q^89 + 336 * q^91 + 1008 * q^92 + 512 * q^93 + 672 * q^94 + 768 * q^96 + 128 * q^97 + 408 * q^98 - 160 * q^99

Introduction

L-functions

Modular forms

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